Yes you can use all the chords from Ab major scale on F minor, assuming you are talking about F natural minor.
The numbering of the chords will be different- F minor is chord I in F minor but chord VI in Ab major.
Most chord sequences in F minor will start with F minor chord etc
Extra info:
However, one chord which is often used in F minor but less often used in Ab major is chord V- C major. This is because a common technique to make a chord sequence sound finished (more in classical music than popular music really) is the perfect cadence- the major V chord (or dominant chord) followed by chord I.
Try playing Eb major -> Ab major- it sounds very final and finished.
Now try C major -> F minor- again, it sounds final and finished.
In major keys, the major V chord (dominant chord) is naturally part of the key so you can use this perfect cadence no problem- however in minor keys you would think that you could only use the minor V chord e.g. C minor in F minor because the F natural minor scale has no E in it but C major chord does.
To get around the fact that C major is not 'naturally' part of F minor, composers will switch to a new scale- the harmonic minor whenever they want to add a perfect cadence in minor keys.
Ab major: Ab, Bb, C, Db, Eb, F, G, Ab Chord V = Eb major
F natural minor: F, G, Ab, Bb, C, Db, Eb, F Chord V = C minor
F harmonic minor: F, G, Ab, Bb, C, Db, E, F Chord V = C major
As you can see Ab major and F natural minor contain the same notes and share exactly the same chords- but F minor you can also swap to F harmonic minor sometimes, which lets you use C major.
This is a lot more info than you asked for but hopefully it shows you that minor keys don't always contain exactly the same notes as the relative major, even though they often do.