Translating "may turn into this"

For "turn into" (as in "transform"), I would use mūtāre in with accusative, as in the very beginning of Ovid's Metamorphoses:

In nova fert animus mutatas dicere formas / corpora;
I intend to talk about people transformed into new shapes;

In Latin, words like "that which was woven" and "this" need a gender. Normally I'd use the gender of the word for "bracelet", but no obvious word for that comes to mind, so I'm defaulting to neuter.

With those choices made, the rest of the translation is straightforward:

In hoc textum mūtet.
A woven thing may turn into this thing.

(For most purposes, you'd want to write the last word as mutet, without the mark over the U; it represents a pronunciation distinction that vanished in later Latin.)