How do I extend the ribbon cable in the photo?
Don't even solder the wire extensions, solder makes stranded wire brittle.

Strip 3cm ends.

Twist the two ends together tightly and clip excess.

Lay the twisted end against the wire.

Slip on a length of heat-shrink tubing.

Use cigarette lighter to shrink the tubing.

Add another layer of tubing if you like.

Practice the technique on scrap wire and pull on it afterward to verify just how strong the connection is.