Solder the core on to the opposite side to the chip (in the opposite corner).

Cut two pieces of the smallest heatshrink - roughly 4mm long.

Slide on to the braid leaving roughly 3mm of braid free at the end where it joins the cable.

Shrink in to place. If your heat gun is a bit powerful, use the soldering iron to supply the heat.

Cut off the braids leaving about 3mm free beyond the heatshrink.

Solder the first braid on to the chip side in the opposite corner to the chip.