chain map from a resolution to another injective resolution induced by linear map is unique up to chain homotopy equivalence

Question

Let $0\rightarrow M\rightarrow E_0\rightarrow E_1\rightarrow...$ be a resolution of a $R-$module $M$.
Let $0\rightarrow N\rightarrow I_0\rightarrow I_1\rightarrow...$ be a injective resolution of a $R-$module $I$.
Then for every linear map $f':M\rightarrow N$, there is a chain map $f$ between the two resolutions which restricts to $f'$.
Is this map $f$ unique up to homotopy equivalence? Well, according to the comparison theorem 2.37 in page 40 of the book 'an introduction to homological algebra' by Charles Weibel it is but I think it should be uniquely determined by chain homotopy instead of chain homotopy equivalence.