I assume those players play games under the same studio, which will be easier to handle your scenario. If those titles are in separate studios, it will need much more efforts.
Players will share one Master Player Accounts within the same studio, which means for each title, they will have separate title player accounts, but under the same Master Player Account. Players can log into Title B with account identities in Title A -- if Title A and Title B are in one studio.
Player Data (Publisher) of a player account can also be shared, any data stored there will be shared among titles within the studio. Hence, you may store some specific KVP in Player Data (Publisher) so that you may give out gifts via checking if this player has some KVP in Player Data (Publisher).
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