###Edit 

(Corrected error in algorithm)

You can reverse the encryption with `Solve`, which can handle modular equations.

    With[{alphabet = Alphabet[]},
      With[{n = Length[alphabet]},
        EncryptChar[char_, a_, b_] :=
          Module[{position, shift, mod},
            position = Position[alphabet, char][[1, 1]] - 1;
            shift = Mod[a position + b, n];
            alphabet[[shift + 1]]];
        DecryptChar[char_, a_, b_] :=
          Module[{position, shift, mod},
            position = Position[alphabet, char][[1, 1]] - 1;
            shift = Solve[a x + b == position, x, Modulus -> n][[1, 1, 2]];
            alphabet[[shift + 1]]]]]

    (DecryptChar[EncryptChar[#, 3, 5], 3, 5] & /@ Alphabet[]) == Alphabet[]
`True`

Note: I also cleaned up you code a bit.