I tried to do the conversion as best as I could, but things went wrong and I could still have things go wrong, so don't rely 100% on this info. Anything I've found out running the car after doing the conversion ill write at the bottom.
It was a ballache to get a good engine, hopefully you have a good engine and everything worked before it came out of the 405.

With the 405 engine on the garage floor the first thing I done was strip down most of the external parts to replace them and drain the oil. The waterpump, oil seals, oil filter and timing belt were changed for new whilst on the floor cause it was easy to do and also with a second hand engine you never know the last time they were checked or in the case of the water pump if the bearings were still good. Doesn't cost much or take long to do and saves a big bill if the belt snapped under load or you have to pull the engine out again cause the water pumps knackered.
The other problem was that the sump gasket was leaking so following the Haynes manual I used instant gasket on the top plate and a new gasket on the bottom. While the sumps off I checked the oil pump gauze and slack in the chain.
I had a Mi16 gearbox from the other engine but decided not to use it cause of the gear ratios, also one of the gearbox linkage arms are different but I modified it to work on a 205 just incase.

You can use the original gearbox off a 205/309 GTi, only thing needed is the correct release bearing. The BE1 gearbox (Lift-up collar reverse) and BE3 gearbox (Reverse behind fifth) have to have the corresponding release bearing as there not interchangeable.
The clutch plate was replaced for a new Mi16 item, but before fitting the gearbox to the engine it needed to have the  sensor hole finished. On the top of the box there is a tear shaped casting with a hole about 1" diameter located over the flywheel, this needs drilling out to fit the body of the TDC sensor, and the smaller hole needs a thread tapped so the sensor can be screwed to the box. After you've done this file the whole top section down about 1.5mm so the sensor sits close enough to the flywheel to get a reading. If you're using a BE3 gearbox then you should already have a sensor hole the right size with a threaded hole ready to take the sensor.

Got the garage cleared out a bit and craned the engine to the front of the car, dropping the engine in from the top was harder than the other engines because of the size of the inlet manifold, but with a bit of persuasion the engine sat on the mounts happily enough. The exhaust manifold was close to the bulkhead but not touching and the inlet manifold comes forward into the space where the radiator should be. First job was to make clearance for the exhaust manifold so I removed the lower engine mount and instead of drilling a new hole which would of been close to the edge of the mount, I took a gamble and chopped the two forks off the mount. The idea was to weld a 15mm rectangular piece of steel in the middle of each side to push the bottom of the engine forward but retaining the original bolt holes. With the bottom mount altered the exhaust manifold fits the down pipe fine but the downpipe needed about an inch cut from the end where it fits into the middle silencer, and a cheese wedge shape taken out near the manifold flange so it tucks under the bulkhead without touching. Ive heard a lot of people have had oil starvation problems from tilting the engine like I've done. Instead they hammer the bulkhead lip inwards to make clearance for the downpipe. I could be fortunate I guess cause mine doesn't suffer pressure any loss on long corners, but im tempted to hammer the bulkhead in next time the engine has to come out and run it at the proper angle.

The inlet manifold is a bitch, it seems to be massive. I guess there are loads of different ways to fit the radiator back into the little bit of leftover space, but I had already made a new bracket on the outside of the engine bay to fit a previous engine and after the time it took to measure and make that I was determined to use it :). The bracket sits about 3.5" away from the bodywork and the radiator cowling sits on the bracket. This spaces it out away from the inlet manifold with out having to cut the cowling. I got a second radiator fan from a guy at work and put that in the cowling with the original one and wired it up to a switch on the steering column. Moving the radiator this way meant that the inside of the bumper had to be cut to make it fit back on the car.

Plumbing the engine in was another mission. Most of my hoses were rotten and not many came with the engine, so I went to my local Peugeot dealer and asked for a price. At nearly £200 to replace 3 hoses I decided to make my own. I adapted as many as I could from the original engines and made a couple of others that ran from the heater matrix. The hose from the heater matrix to the thermostat changes diameter at the two ends, so I bought two correct diameter pipes and joined them in the middle using plumbing bits from B&Q. It cost me less than £10. Then I bought a flexible hose from Halfords which fitted fine between the water thermostat and the top of the radiator because this hose needs to bend in a 'S' shape, this also cost a tenner and meant I saved my self around £180 :) The brake vacuum hose for the servo fits on the inlet manifold where the rubber blanking piece is, right next to where the hose for the idle speed valve is located. To get the water oil cooler working, one pipe used to come from the 405 radiator but there's no T piece in the 205 system to take a feed from. Order a Citroen BX diesel bottom radiator hose and this replaces the 205 bottom hose and adds a T piece for the oil cooler.

Things I Know Now

Using instant gasket didn't cure the leaking sump. The stuff recommended to me actually dissolved and leaked worse after I tried to fix it. So I bought a pair of gaskets and used them on the top and bottom of the spacer. The top one needed two holes punched in the opposite edges for the locating dowels. Knocked it back together again and its not leaking anymore.

Exhaust manifold snapped. When the car first ran it sounded like a tappet was noisy, and after a month or so it developed into a blowing from the manifold/downpipe flange. Replaced the downpipe gasket and refitted but the noise was just as bad, and you could feel exhaust fumes near the joint. Took the car to Santa Pod and the manifold snapped into two pieces at the joint. Luckily I had another manifold at the house and this also had cracks in but not as bad, so it was welded up and fitted. Seems like the manifolds are a weak design so worth checking before the engine goes in.

Gearbox Diff exploded and the pinion gear shattered into many pieces coming through the gearbox into the clutch. This was an original BE1 box that had covered about 100,000 miles. Im now using a BE3 box off a 309 GRi which has lasted so far.

Magnex front silencer kept knocking on the floor of the car or hitting speed ramps, no matter how I tried to make it fit. In the end I took the middle section out and made a straight through pipe with a 2 foot length of flexi pipe in between. The flexi pipe takes the strain out of the system by allowing some movement and I've also heard since that removing the front silencer can increase power on a 205 mi16.

Hammered the lip on the bulkhead upwards to sit the engine at correct angle, only took 5 minutes and the downpipe has plenty of clearance now. Should of done this in the first place as it would of saved a lot of messing about, and it should reduce the strenght of the bulkhead.