Cyclic groups of the same order are isomorphic. The mapping f:G→G′, defined by f(ar)=br, is isomorphism. Therefore the groups are isomorphic.

Are two cyclic groups isomorphic?

Two cyclic groups of the same order are isomorphic to each other.

Can a cyclic group be isomorphic to a Noncyclic group?

The answer to this question claims that these two groups are isomorphic but I believe this is false. Firstly, surely it must be impossible to have a non-cyclic group that is isomorphic to a cyclic one.