Transfer map definition I have been reading Brown's Book on cohomology of groups and now he is defining the transfer map, and for that he stataes that for any $H \subset G$ we can regard both $H_*(G,-)$ and $H_*(H,-)$ as homological functors on the category of $G$-modules , and yes this I think I can see why its true, but then he says that they are both effaceable in positive dimensions, now i know $H_*(G,-)$ is because we can either take projective modules or modules of the form $\mathbb{Z}[G]\otimes M$, and I know that $H_*(H,-)$ will be effaceable in the category of $H-$modules but i dont see how we can see that its also effaceable on the category of $G$-modules.Thanks in advance.

As noted in the comments, this follows because $\mathbb Z[G]$-projectives are $\mathbb Z[H]$-projective. 
Now to prove that, it suffices (since any $\mathbb Z[G]$-projective is a direct summand of a direct sum of those) to prove that $\mathbb Z[G]$ is $\mathbb Z[H]$-projective. 
But any coset decomposition $G= \coprod_{x\in A}Hx$ yields a direct sum decomposition $\mathbb Z[G] \cong \bigoplus_{x\in A}\mathbb Z[H]$ as left $\mathbb Z[H]$-modules, so we are done. 
