The lucky couple: a clearanced universal remote and a shake flashlight.

Extract the guts.

Chop the superficial bits from the top of the shake coil assembly to fit the remote casing.

Chop a hole in the remote casing to fit the coil assembly. I used a mini table saw, but a Dremel would work better.

Remove the capacitor from the circuit board. I started putting double-sided tape on it to stick it on, but you can wait until step 15.

Prepare some wire to connect the coil to the circuit board.

Ready one end of the wire for the coil connections.

Solder the connections.

Solder a separate set of wires to the output of the diode bridge (where the capacitor was). You can snip off the unused portion of the board as long as you don't get rid of any important bits.

Solder the coil extension wires to the coil input; the polarity doesn't matter.