We discovered a strongly lensed (mu >40) Lya emission at z=6.629 (S/N~18) in the MUSE Deep Lensed Field (MDLF) targeting the Hubble Frontier Field galaxy cluster MACS~J0416. Dedicated lensing simulations imply that the Lya emitting region necessarily crosses the caustic. The arc-like shape of the Lya extends 3 arcsec on the observed plane and is the result of two merged multiple images, each one with a de-lensed Lya luminosity L<~2.8 x 10^(40) erg/s arising from a confined region (< 150 pc effective radius). A spatially unresolved HST counterpart is barely detected at S/N~2 after stacking the near-infrared bands, corresponding to an observed(intrinsic) magnitude m_(1500)>~30.8(>~35.0). The inferred rest-frame Lya equivalent width is EWo > 1120 A if the IGM transmission is T(IGM)<0.5. The low luminosities and the extremely large Lya EWo match the case of a Population~III star complex made of several dozens stars (~ 10^4 Msun) which irradiate a HII region crossing the caustic. While the Lya and stellar continuum are among the faintest ever observed at this redshift, the continuum and the Lya emissions could be affected by differential magnification, possibly biasing the EWo estimate. The aforementioned tentative HST detection tend to favor a large EWo, making such a faint Pop~III candidate a key target for the James Webb Space Telescope and Extremely Large Telescopes.
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