It's been my experience that when you switch horns, you may (or may not) need to switch altissimo fingerings. I don't think I've ever used the forked F on alto at all.
For an altissimo G on alto, I usually do octave key, 1 and 3 (left hand), 1 and 3 (right hand) and side Bb key. For altissimo G#, I move the side Bb key up to the side C key.
For an altissimo G on alto, I usually do octave key, 1 and 3 (left hand), 1 and 3 (right hand) and side Bb key. For altissimo G#, I move the side Bb key up to the side C key.