Complete Max-SAT solvers are able to return the optimal value of an input instance but they do not provide any certificate of its validity. In this paper, we introduce for the first time a Max-SAT proof builder, called MS-Builder, which generates Max-SAT proofs under the particular form of a sequence of Max-SAT equivalence-preserving transformations. To generate a Max-SAT proof, MS-Builder iteratively calls a SAT oracle to get a SAT refutation which is handled and adapted into a sound refutation for Max-SAT. We also propose an extendable tool, called MS-Checker, able to verify the validity of any proof using Max-SAT inference rules.