This is one of those details that differs between the show and movie. In the movie, all the symbols on each of the two gates are unique. They show constellations in the sky over the gate's planet. So the Abydos gate has Abydos constellations, not Earth constellations. In the show, all gates have 38 identical symbols, with a 39th unique symbol which is the point of origin.
If we were to imagine an alternate version of the film's events having played out where the TV show's rules were in place, once Jackson determined the address for Earth while on Abydos, then that same address could be used by every SG team in the future, they simply need to memorize the first 6 symbols, and then dial whatever their gate's point of origin symbol happens to be. That's how the gate system works in the show. The first 6 symbols in the 7-symbol address are essentially the coordinates for the destination gate. Then the last symbol is the gate's unique point of origin symbol.
It's a given that everyone who goes through the gate has Earth's coordinates memorized, as otherwise they would be stranded.