Position the rectifier board at the bottom of the coil assembly.

Protect the soldered coil wire connections with electrical tape.

Optional (part 1): Add add a Zener to the diode bridge output to protect from over voltage (too much shaking...).

Optional (part 2): Fit and solder diode to the output and snip off excess.

Add a few layers of double-sided foam tape to the capacitor and trim to size.

Stick the capacitor on the bottom. Make sure there is room for the entire assembly to fit into the remote casing; if it will not, cut a hole in the casing to accommodate the capacitor.

Grab your remote innards.

Remove the battery contacts from the remote circuit board and attach the wires from the diode bridge output.

Assemble everything, ensuring it all fits nicely.

Prepare to glue the bottom cap on the coil assembly. I used this glue because it contains ethyl cyanoacrylate which has some flexibility.