  Let F be a non-Archimedean local field of residual characteristic p, and
{\ell} be a prime number different from p. We consider the local
Jacquet-Langlands correspondence between {\ell}-adic discrete series of GL(n,F)
and an inner form GL(m,D). We show that it respects the relationship of
congruence modulo {\ell}. More precisely, we show that two integral {\ell}-adic
discrete series of GL(m,D) are congruent modulo {\ell} if and only if the same
holds for their Jacquet-Langlands transfers to GL(m,D).
