I take it you'll be coming in from LHR on AA137. You'll clear customs and immigration in T4 and will then collect your luggage to recheck it to your final destination. I'm assuming you'll just walk from baggage claim upstairs to get your luggage rechecked at the AA counter. If that's the case you'll have to reclear security (which shouldn't be bad at that time of day) and take the bus to the remote AE terminal. If your flight from London is on time you should make it.

Hopefully someone who has actually done this kind of transfer can shed some more light on the process.