Here is the SFO terminal map:
http://www.flysfo.com/maps/interactive-maps
As you mentioned there is a secure connector between Terminal 3 and International Terminal G. The International Terminal is split, with G gates on one side and A gates on the other side but in the middle is the main hall which is outside the secure area so you cannot (I believe) walk directly across the international terminal through the main hall to the other side without leaving and re-clearing security.
The only way (I suspect) this might work is to walk all the way around the airport from International G to T3 to T2 to T1 to International A, and I don't even know if that is possible.
One other possibility is that for now (while United has some flights from T1 during renovations) he could potentially take a United shuttle bus from either the International terminal or T3 (both inside security) to T1 where United has a few flights. Then, if there is a connector from T1 to International A he could make it work. But, I suspect it might be faster just to leave the secure area, walk across to A and re-clear.
Shuttle info:
http://www.flysfo.com/flight-info/al...ted-operations
Transfer Bus Operations
United Airlines operates bus service between Terminals 1 and 3. Buses run between:
Gate 39 in Terminal 1 and Gate 71A in Terminal 3
Gate 39 in Terminal 1 and Gate 87A in Terminal 3
Buses run every 4-5 minutes. Travel time between stops is approximately 4-5 minutes.
- See more at:
http://www.flysfo.com/flight-info/al....spr1q5bi.dpuf
http://www.united.com/cms/en-us/trav...elnotices.aspx
San Francisco terminal information
United flights from San Francisco International (SFO) depart from Terminal 1, Terminal 3 and the International Terminal. Ticketing, check-in and baggage drop for all flights are located at Terminal 3.
You may proceed through security at Terminal 3 and, if you are departing from Terminal 1, take the shuttle bus from Terminal 3 to Terminal 1. If you are departing from Terminal 1 and have already checked in, do not need to see a United representative, and do not have any bags to check, you may proceed through Terminal 1 security with your boarding pass.
Shuttle buses depart every five minutes from Terminal 3 (Gates 71A and 87A) to Terminal 1 (Gate 39). For elevator access to a bus stop, please use Gate 87A.