Hey there. Expansions do not transfer over cross-save. He has access to Shadowkeep, Beyond Light and Witch Queen due to a current PS/PC promotion that makes them free to access until The Final Shape (I think the first two will remain as owned even when this period ends). However otherwise, yes it is correct that he is unable to access Forsaken and Lightfall on PC. The platforms sell DLC licences and all of them want their cut. If you want to play them on PC then you need to own them on whichever storefront you play the game on.