The ignition system of the ABA 2.0L engine uses a crank sensor as a result its distributor is not compatible with the ignition system of the A1. You have three basic options for dealing with this:
It may be possible to transplant the trigger wheel and sensors from your A1's distributor into the ABA's distributor (I don't have enough details on this so I'm not sure.) Installing the A1's distributor has its own problems, the diameter of this distributor body is smaller than that of the 2.0L so you need a bushing to take up the extra space. The drive gear on the distributor are also different so you must either switch the gear on the distributor or switch the intermediate shafts. If you chose to switch intermediate shafts the 1.8L shaft must be machined to allow clearance for the longer throw of the ABA connecting rods. Conveniently, reasonably priced kits can be purchased to install your 1.8L distributor into an ABA block.
The ABA block is about 16mm tall then the 1.8L block this can result in the exhaust system hitting the underside of the car. There are a few ways you can deal with this:
As mentioned above the ABA block is taller then the 1.8L block so the timing cover of the 1.8 will not fit on the new engine. The timing cover of the 2.0L is not usable without modification because it covers bolt holes that must be used for the A1 engine mount. You have a few options here:
The 2.0L engine has a crankcase vent located where the warm-up regulator (a.k.a. control pressure regulator) would be located in A1. The prefered way of dealing with this vent is to remove it, install a block-off plate and install the warm-up regulator in its normal location.
There are a couple of installation details worth mentioning.
The recommended head gasket for this application is the 2.0L-16 valve head gasket although the 1.8L head gasket will also work provided the engine doesn't have oversized pistons.
Timing belt, use an ABA timing belt on this engine, due to the slightly taller block, a 1.8L timing belt would be too short.
Do yourself a favour and install the intake manifold after you,ve installed the engine, clearances with the rain tray are pretty tight. Install the throttle body after you installed the engine (same reason). It is necessary to bend back the rain tray to make room for the throttle linkage.
And finally, although the target audience of this website is people installing an ABA block into an A1, much of the info presented here applies to A2's as well and I often receive questions from people doing an A2 installation the most common of which is "What downpipe do I use?" or "Can I use the stock downpipe?. I've never done one of these installations into an A2 so any info I've got on this is second hand but I've corresponded with numerous people regarding this and the general consenus seems to be that unlike an A1 installation, there are no clearance issues with the downpipe in an A2. You can use the stock downpipe or whatever other downpipe or header would normally fit into an A2.