Originally Posted by
Djokison
If your LHR-MIA flight is on BA, make sure your bag is checked through to Jamaica. You will not have to pick up your bag upon arrival in MIA and the bag will be on the Jamaica flight the next day.
If however, you're flying AA across the pond, you'll have to pick up your bag from baggage claim and go through customs with it. I don't know if AA will allow you to drop off the bag immediately that night. (I don't think they will, but you can always try.)
It's worth noting that MIA is notorious for things mysteriously disappearing from checked luggage. Leaving your bags overnight will no doubt increase that risk. (I however, have not experienced that the 1-2 times I left a bag there overnight)
While I've never transited the USA en route to a 3rd country, I've never arrived on a USA-bound international flight and not had the entire plane emptied into immigration and customs/ag which required claiming your bags. There's usually/always? an area post customs to re-check bags that are checked to a final destination, but I've never heard of not even having to claim bags.