What I am saying at this point that while stranded wire is much preferred over solid, since they have already used the cheaper solid wiring, then you can use it as well.
If you want to re-use the speed box to extend the circuit, you have to use solid wiring as the boxes use the insulation-displacement technique to attach the wiring.
But if you want to use stranded wiring, you will have to go to a more conventional outlet, which will also mean you have to install an electrical box - which is larger in size - which means you will have to cut the panel out.
Here is a PDF on how to install speed boxes:
http://www.hubbell-wirecon.com/liter...ationGuide.pdf
Here is a video that might be helpful:
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