Knot quandle homomorphism

Question

If you have a map that sends surjectively the generators of a knot quandle $\langle x_{i} , \ldots , x_{m} \mid r_{i} (x_{1} , \ldots , x_{m} ) \rangle$ to $\langle y_{i} , \ldots , y_{m} \mid s_{i} (y_{1} , \ldots , y_{n} ) \rangle$, and well as the relations $f(r_{i}(x_{1} , \ldots , x_{m} )) = s_{i}(f(x_{1} ) , \ldots , f(x_{n}) )$, then do we have a knot quandle homorphism (analogous to Von Dyck's Theorem)?