Regular little shutterbug aintcha XJKEE ....
Just the one piccy would have done for me .... I can see its bigger than your trailer by the first pic ....
Whats under the plastic caps ... push on hose fitting barbs ???
If so ... that would suggest it is an oil cooler but that tube dia. looks a bit small ???
All you can do is run some oil through it and see if you think the flow is fast enough to match the gearbox ...
....... and see if it leaks - got a air compressor you can wind the pressure down on ???
Next step would be to fit it on someone elses XJ and see if it works ...
Maybe a AJOR member auto shop trady can recognise it ???