Can I swap battery cells 6S to 7?

Actually, I'm going to disagree with @corbanizer and suggest that there's no real reason it wouldn't work. The base chemistry of the battery cells is the same; they both take the same charging voltage at roughly the same rate and the BMS will regulate that. I'm guessing he 6S battery is slightly smaller so it will have a marginally shorter run time, but I doubt it's enough to make a significant difference.

As Corban said, the best strategy would be to simply buy a new 7 battery, but honestly there's no reason your plan won't work. The only catch here could be physical limitations; the electrodes coming out of the 6S cell have to be similar enough in geometry that they can be connected to the 7's BMS, and the physical size has to be such that it will fit into the 7's battery compartment and let the connector plug in.

If you do go ahead with this, be sure and come back and show us pictures of either the process or the finished product and let us know how it worked. Success stories are always appreciated, and we can usually learn something even when things don't go as planned.

Oh, one last thing; the best method for working on batteries is using a spot welder, as it minimizes the heat the battery cell is exposed to. If you don't happen to have one of those little devices, then solder carefully and use as little heat as possible; just get them tacked on so there's a good electrical connection.