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When solving constraint problems, symmetry handling is a crucial optimization. However, it is well-known that several preprocessing methods and encodings change the syntactic symmetries of the problem, and hence make it more difficult to exploit the symmetries that were present in the original problem. As a consequence, when currently using such methods, one should either handle the symmetries on the original specification or live with the fact that efficiency is lost since this structure is no longer visible. In this paper, we take a different approach: we develop a framework in which symmetry information is explicitly part of the specification and can be passed along through different transformations. One subtle, but important point in this respect is that transformations can change the set of variables. We study theoretical properties of transformations that preserve symmetry information, and we analyze existing transformations from the literature in this framework. We experimentally evaluate our framework on translations of pseudo-Boolean constraints into CNF and show that in practice, simply passing on the symmetry information can lead to significant speed-ups in solving time.