You must know how it works for barre chordes right? Well its the same for scales. Anything than doesn't contain an open string on a guitar can be transposed up to the next note into a different key. That is a rule on the guitar.
According to what I think (keyword THINK) you are saying, moving an A minor melodic scale up one fret means it cant be a melodic minor any more. That is incorrect. It would just become an A# melodic Minor.
If I misunderstood you, please tell me.