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Indeed, this is broken. Note that it works fine with the identity morphism

sage: fR = Hom(R, R).one()
sage: fR
Identity endomorphism of Power Series Ring in x over Integer Ring
sage: fR(1 + x + O(x^2))
1 + x + O(x^2)

But not for the lifted identity

sage: fZZ = Hom(ZZ, ZZ).one()
sage: fR2 = Hom(R, R)(fZZ)
sage: fR2(1 + x + O(x^2))
1 + x