Take a symmetric Nakayama algebra with Kupisch series [3,3]. (see for example the book by assem simson skowronski in the chapter about nakayama algebras for the meaning) Then $Hom(e_0 A, soc(e_1A))=Hom(e_0 A, S_1)=0$, but $Hom(e_0A , e_1A)$ is nonzero and thus has nonzero socle.
Mare
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