IAE V2500 engines are assembled in both Middletown (part of P&W's operations near East Hartford, Conn. USA) and Rolls-Royce's plant in Derby UK.
CFM are put together in both Snecma's Villaroche facility in France and at GE's plant in Evandale, Ohio USA.
All IAE production goes to TLS or HAM.
CFM56-5B go to TLS or HAM and some CFM-56-7B still go to Seattle!
Hope this helps.