Can one do it?
I'm trying to prove that $S^{-1}I$ is an injective $S^{-1}R$-module whenever $I$ is an injective $R$-module.
So I need to start with a situation where I have:
(i) $S^{-1}R$-modules $M,N$. (ii) a homomorphism $j:M\to S^{-1}I$ (iii) an injective homomorphism $i:M\to N$.
From this I want to strip the situation down, (by embedding $I\to S^{-1}I$).
I almost have a solution but I think it comes down to being able to interpret $M$ as an $R$-module. Can this be done or do I have to remove elements of $M$ to make it work?