Is there a function to test for isomorphism between two
ag groups? This would maybe solve my problem, but I
did not find such a function. Moreover this functions
should also provide an isomorphism mapping generators
of one group to as short as possible expressions in
the generators of the second group.

How "big" are the ag groups you are interested in (composition length,
size of commutator factor group)? There is a way to use 'Complements'
to find isomorphisms between ag groups, but this will only work if the
groups are not too big.

best wishes
Frank Celler