I literally just converted my FAA to TC. It took me about to months of waiting time.
Worth noting that TC and the FAA has bilateral agreement, but no such agreement exists for EASA/UK CAA license, so anyway you must pass a written exam (not even a conversion exam like the FAA to TC license) and a flight test, which means there is no waiting time. If you have the hours, and pass the written and flight test - your TC license will be issued on the spot.