Module amenability of the projective module tensor product

Let S be an inverse semigroup with the set of idempotents E. In the current paper, we show that the projective module tensor product -module amenable when S is amenable. This could be considered as the module version (for inverse semigroups) of a result of Johnson (1972) which asserts that for any (discrete) amenable locally compact group G the projective tensor product is amenable