Converting from magnetic scalar potential to magnetic vector potential

For a given elementary dipole source of strength $mathfrak{m}$ the answer is very simple: $$textbf{A} = frac{1}{4pi} frac{mathfrak{m}times textbf{r}^0}{r^2} $$ and $$phi = frac{1}{4pi} frac{mathfrak{m}cdot textbf{r}^0}{r^2}$$ The induction field is then $$textbf{B} = text{curl}textbf{A} = -text{grad}phi = frac{1}{4pi} frac{-mathfrak{m}+3mathfrak{m}cdot textbf{r}^0textbf{r}^0}{r^3}.$$ Of course, for a continuous dipole distribution you can sum this with an integral. Anyhow, first you have to find the dipole field from the scalar potential and then you can get the vector potential.