As for parts...
For any electric conversion, you need the motor, some form of gearbox, a motor controller, a battery pack, and some form of battery management system. No difference here; there's also a huge amount of detail to understand beyond that...
Following edited after clarification by original poster:
With the understanding that the entire original powertrain stays intact and continues to drive the rear wheels, to add electric drive of the front wheels you also need a suitable gearbox, halfshafts with CV joints, and front hubs which accommodate being driven.
Since the engine is in the way, the only easy solution is BMW's stock parts from an all-wheel-drive BMW 3-series (model ending in "xi") - final drive unit (differential), and halfshafts, and hub assemblies. The electric motor would probably need to sit beside the output of the transmission, where the transfer case is in the stock AWD configuration... although there still won't likely be enough space. Since you are not going through the BMW transmission you also need a reduction gearbox.. or you could use the electric motor output directly to the front final drive, at a substantial performance penalty especially at lower speeds).
Finally, to make this a functional hybrid - rather than just a car with two unrelated drive systems - you need some way to produce electricity from the engine. Normally in hybrid adaptations of conventional powertrains a motor-generator is sandwiched between the engine and transmission; it acts as a generator for regenerative braking of the rear wheels, as a generator when desired to charge the battery from the engine or shift power to the front wheels for traction or handling, and as a motor to use battery power instead of engine power (although you say you don't want to do this). This is easy when the transmission manufacturer designs this piece, but it doesn't exist for the GM 5L automatic used in this car, and is very unlikely to exist for the manual transmission as well.
The end result, with hybrid drive to one axle and electric-only drive to the other, is a similar configuration to the Highlander/RX and RAV4/NX hybrids from Toyota/Lexus, the current RL, MDX, Pilot, and NSX from Honda/Acura, and some exotics. In all of these, electric drive is available to the engine-driven axle. Also in all of these cases, the electric-only axle is at the other end of the car from the engine, so packaging the electric motor and gearbox is easier.