  Duke and the second author defined a family of linear maps from spaces of
weakly holomorphic modular forms of negative integral weight and level 1 into
spaces of weakly holomorphic modular forms of half integral weight and level 4
and showed that these lifts preserve the integrality of Fourier coefficients.
We show that the generalization of these lifts to modular forms of genus 0 odd
prime level also preserves the integrality of Fourier coefficients.
