Welcome to Restoration-Mini!!
The car came with an MGB oil cooler, which fits fine over in the left (driver's) side of the grill opening. It doesn't touch the starter tho. Dan found us an original Innocenti oil cooler which mounts completely differently than the MGB one so I'm going to have to make some brackets for it but I anticipate it will go in the same place. I think I need to mount the radiator and alternator before I try and figure out the brackets for the oil cooler.Here are couple of "before" pics....I'm pretty sure I can do better.....I can't believe the hose with the yellow bands doesn't leak since there are no clamps on it! No matter, I'm going to have new hoses made anyway.
I finally figured out how to mount the Italian oil cooler Dan found for the Inno - if I turn it over and have the hoses come out the bottom there's plenty of room. Dunno why I didn't think of that before, but the old one was mounted the other way so I tried to follow that.