  We present an analysis of HI Lyman-alpha emission in deep VLT/MUSE
observations of two highly magnified and extended galaxies at z=3.5 and 4.03,
including a newly discovered, almost complete Einstein ring. While these
Lyman-alpha haloes are intrinsically similar to the ones typically seen in
other MUSE deep fields, the benefits of gravitational lensing allows us to
construct exceptionally detailed maps of Lyman-alpha line properties at sub-kpc
scales. By combining all multiple images, we are able to observe complex
structures in the Lyman-alpha emission and uncover small (~ 120 km/s in
Lyman-alpha peak shift), but significant at > 4 sigma, systematic variations in
the shape of the Lyman-alpha line profile within each halo. Indeed, we observe
a global trend for the line peak shift to become redder at large radii,
together with a strong correlation between the peak wavelength and line width.
This systematic intrahalo variation is markedly similar to the object-to-object
variations obtained from the integrated properties of recent large samples.
Regions of high surface brightness correspond to relatively small line shifts,
which could indicate that Lyman-alpha emission escapes preferentially from
regions where the line profile has been less severely affected by scattering of
Lyman-alpha photons.
