You may need to fit a different cat flap that only lets
'keyholders' in! lol. Some are operated by a magnet on the collar & (more expensively) some by an infra-red device also hung from the collar. Both will easily replace an existing cat flap.
As your girl is getting older you will probably find she goes out less & less - partly due to this other cat's presence. She just doesn't need the hassle.
'Big boy' is probably off finding 'brides' since spring has sprung. If you think he's a stray it would be well worth your while catching him ( trap him in your kitchen) & then getting the local Cat's Protection to collect him. They will blood test for feline 'aids', innoculate, neuter & micro-chip him before finding him a new home where he will recieve appropriate care. Then your girl can enjoy her life again - it will take quite a long time for her to rebuild her confidence.
If you think he may belong to some one then place a collar with a note on it & see if you can come to a 'time share' arrangement with his owner.