I connected through LAX two weeks ago (BA to AA).

Your father needs to clear US immigration (which is much faster now due to US Customs and Border Protection kiosks (APC) in operation), claim bags and clear customs at TBIT. Before getting landside at TBIT he will pass AA staff that ask if he is connecting to an AA flight. In the affirmative, they will check the luggage tags, scan them and bags will be put on a conveyor belt, i.e. this is where bags are dropped for the connecting flights. Besides this, AA has no recheck area at TBIT, everything is handled at nearby T4 (two minutes walk from TBIT - turn right when you walk out of TBIT).

Your father is able to clear security/TSA and go airside at TBIT or T4. The security lines at TBIT were very long so we walked to T4 and went airside there. There was a line at T4 but it took 10-15 min at the most to clear security/TSA.

Most likely the AA flight will depart from T4. If your father decides to clear security/TSA at TBIT he is able to walk from TBIT to T4 via the new "connector" that links the two terminals.