A ring R is called a right FPF ring if every finitely generated faithful right R-module is a generator (in the category of right R-modules). T. G. Faticoni [J. Algebra 107, 297-315 (1987; Zbl 0618.16021)] has shown that a semiperfect right FPF ring has a semiperfect right self- injective classical (left and right) ring of quotients. The current paper extends his investigation into the connection between semiperfect FPF rings and self-injectivity. Let R be a basic semiperfect ring, i.e., R/J(R) is a direct sum of division rings, and let \(R=e_ 1R+...+e_ mR\) be a decomposition into primitive idempotents. The author shows that R is right FPF if and only if (i) every partial homomorphism from \(e_ iR\) to \(e_ jR\) (i\(\neq j)\) extends to a homomorphism from \(e_ iR\) to \(e_ jR\), (ii) every partial homomorphism f on each \(e_ iR\) extends to an endomorphism in \(e_ iR\), provided f is not monic, (iii) given partial homomorphisms f, g on \(e_ iR\) then either \(f=gr\) or \(g=fr\) for some r, (iv) each \(e_ iR\) is uniform, and (v) each nonzero right ideal of R contains a nonzero two-sided ideal.