Off-diagonal Heisenberg matrix element calculation

1. The problem statement, all variables and given/known data

J would like to calculate the off-diagonal matrix element of the Heisenberg spin interaction Hamiltonian between 2 atomic states. S1, S2 are the spin operators with quantum number S, and the states are labelled by m1, m2 the z-component quantum numbers of S1, S2 respectively.

2. Relevant equations

H = -2JS1.S2

<S,S-1|H|S-1,S> = ?

3. The attempt at a solution

I have used the ladder operators for the case S=1/2, but how do we proceed in the general case?

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