This is the original plastic tunnel for the air intake, that takes the air all the way in front of the water radiator and somewhat probably sucks warm air from the inside of the engine compartment.
When I installed the oil cooler I made the decision to cut it over and shorten it, to get better and colder air to the engine and to provide a good rout, for the oil hoses to the oil cooler and in addition to this modification, I acquired a new genuine/used BMW air filter box that has an extension snout/pipe for fresh air intake that is taken from the left inside of the wing. The inner side of the wing has a purpose built hole for this setup. Not all engines need this extra air intake that is depending on geographical circumstances and the size of the engine.
Although I cut a large chunk of the intake it still uses all the original fasteners (exempt for the peace I removed) to hold it firmly in place.
With this setup, there is no fear of getting water into the engine or the air filter.
If you look at the picture "Engine Oil Cooler Final Setup_E39_M52b25" you can clearly see the changes.
The picture was taken back in May 2018 when I had the car painted, at this point I had not detailed the paint, so it looks a bit wavy and ruff with orange peal but it turned out fine, after buffering and polish.