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We continue the development of X-ray tomography in sub-Riemannian geometry.Using the Fourier Transform adapted to the group structure, we generalize theFourier Slice Theorem to the class of H-type groups. The Fourier Slice Theoremexpresses the X-ray transform as the composition of a Fourier restriction andmultiplication operator. We compute the spectral resolution for the resultingoperator-valued multiplier, which we use to show that an integrable function onan H-type group is determined by its integrals over sub-Riemannian geodesics.We also relate the support of the X-ray transform $If$ to the support of $f$ infrequency space. These results given explicit answers to the injectivityquestion in a class of geometries with an abundance of conjugate points.

The sub-Riemannian X-ray Transform on H-type groups: Fourier-Slice Theorems and Injectivity sets