[morzh]

>> Yes. Ball up in a corner and cry very deeply?

It's a good start

Then try to get off the outer shell, take pen and paper, mark the view (top/bottom, to have a reference) and make a sketch, showing how the wire wraps around starting from the lug it is soldered to.
Count the turns.

Good news is, this is a small coil and I doubt there is more than 100 turns.
Get the wire gaged, then buy the appropriate magnet wired (unless you have it already) and simply wind the coil.

Then wrap it into ... Kapton would do.