Let X and Y be smooth varieties over a finite field F. Let R be a complete DVR of unequal characteristic with residue field F. I have the following question:

If f is a morphism from X to Y, is it possible to choose formally smooth R-formal schemes, $\mathfrak{X}$ and $\mathfrak{Y}$, whose special fibres are X and Y respectively, together with a morphism g from $\mathfrak{X}$ to $\mathfrak{Y}$ which lifts f under the natural specialization maps?