Slide the housing back over the magsafe connector. It goes on either way round (there is a hole for the led on both sides.

Squeeze in place with the pliers. If it doesn't fit over the circuit board fairly easily, check that you don't need to file down the solder joints some more.

Slide the first of the pieces of heatsink up against the plastic housing.

Keeping it tight, shrink it in place. This is important to help avoid a future failure.

Repeat with the outermost piece of heatshrink.

Try powering it up! Remember that it will take a few seconds before the LED illuminates.

Orange light - success!

Abrading the top of the casing and applying a big blob of hot-melt glue seemed to provide more permanent, if less elegant, strain relief!