Answer to similar questions: here
Two useful links with information that should be useful:
link1
link2
Mapping a given FIGI to a RIC is almost impossible without a BBG license . Openfigi.com will povide basic Bloomberg data on the FIGI and that may contain exchange ticker but it cannot be relied on . Openfigi will accept ISIN Cusip as input so you can build a cross reference from RIC/ISIN to FIGi. However this means to map any FIGi from say the LSE you have to map ALL the ISIN/RIC for the LSE and refresh this everyday And if.ypu want all markets and all assets you have to do this globally. Magtia provide exactly this service for LSEG / Refinitiv clients