Would anybody know the parent major scale of F sharp minor 7 flat 5?
There are two likely choices for the parent scale of an F♯-7(♭5) chord, also known as an F♯∅ or half-diminished chord.
This chord can be built on the seventh degree (or the Locrian mode) of the major scale, meaning that G major could be thought of as the parent scale for this chord. From F♯ Locrian this gives:
F♯ A C E G B D 1 ♭3 ♭5 ♭7 ♭9 11 ♭13
But you can also build this chord on the sixth degree (or the Locrian #2 mode, or the half-diminished mode) of the melodic minor scale. This would make the A melodic minor scale a parent scale of the half-diminished chord. From F♯ Locrian #2 this gives:
F♯ A C E G♯ B D 1 ♭3 ♭5 ♭7 9 11 ♭13
Note that the only difference between these two approaches is in the 9th. The Locrian mode from the major scale provides a lowered 9th; this is sometimes called an "avoid" note since it is a half-step above a chord tone and is harmonically unstable. The Locrian #2 mode from the melodic minor scale provides a natural 9th. None of the upper extensions are a half-step above a chord tone, so there are no "avoid" notes here.