The Graded Classification Conjecture states that for finite directed graphs E and F, the associated Leavitt path algebras L_k(E) and L_k(F) are graded Morita equivalent, i.e., Gr-L_k(E) approximate to _gr Gr-L_k(F), if and only if, their graded Grothendieck groups are isomorphic K₀^gr(L_k(E)) congruent to K₀^gr(L_k(F)) as order-preserving Z[x,x^-1]-modules. Furthermore, if under this isomorphism, the class [L_k(E)] is sent to [L_k(F)] then the algebras are graded isomorphic, i.e., L_k(E) congruent to _gr L_k(F). In this note we show that, for finite graphs E and F with no sinks and sources, an order-preserving Z[x,x^-1]-module isomorphism K₀^gr(L_k(E)) congruent to K₀^gr(L_k(F)) gives that the categories of locally finite dimensional graded modules of L_k(E) and L_k(F) are equivalent, i.e., gr^Z-L_k(E) approximate to _grgr^Z-L_k(F). We further obtain that the category of finite dimensional (graded) modules is equivalent, i.e., mod- L_k(E) approximate to mod L_k(F) and gr-L_k(E) approximate to _gr gr-L_k(F).