We present an analysis of |${\rm H\,\rm{\small {I}}}$| 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 allow 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 (⁠|$\sim120$| km s−1 in Lyman |$\alpha$| peak shift), but significant at |$ \gt $|4 |$\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.

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