Folding a tallis for next Shabbos

Hi,

One may not clean clothing on Shabbat, and this applies to non-laundering actions which make clothing better suited for wearing. This may apply to folding clothing, too, although justifications are offered for folding which does not create a lasting crease, or for folding which does not improve the appearance of the garment. However, the consensus of authorities is that one may not fold a garment on one Shabbat to prepare it for the following Shabbat, as in the case of folding a tallit after davening. One may not prepare on Shabbat for after Shabbat.

(Rivivot Ephraim 1:229 - see more there)

Have a great day,
Mordechai