Inner tube valve cut from stretched rim tape? I was trying to fix my sisters flat tire to make some money by charging her fees cheaper than the bike shop.

I found the leak to be on the actual valve piece. Near the base there is a small cut looking to have generated from wear and tear. Looking at the bike wheel rim it came from the rim tape was stretched into an oval around the hole, with one side of the metal hole exposed to rub against the inner tube valve (presumably what caused the cut). 

Only parts of the rim tape were stuck to the rim so I assumed it was meant to move and completely ran a finger beneath it all the way around... On the opposite side of the rim tape next to the whole where the valve piece is threaded through is a fold where the rubber rim strip has gathered around that side of the hole as it stretched.

I tried putting some tape around the cut on the inner tubes valve stem as a quick fix, but overnight the tube deflated somewhat. 
Instead of just replacing the inner tube (I assume this would only work for a while given the issue has not been addressed) I was wondering what would be the best fix?  

Bearing in mind she will probably only pay me $10.
Several fixes


If you have tools, smooth off the cut edge of the hole where the butyl rubber tube touchs it.  A tiny file, or careful use of sandpaper to take the sharp edge off would help.
Reinforce the rim tape with paper masking tape.  Two layers around the whole rim would reinforce the existing tape, with overlap 100mm either side of the valve hole.  As long as the tape sits in the well/valley and has no way to interfere with the tyre's bead/hooks then its okay.   To get the valve through, cut three slots across the hole making an asterisk pattern, and leave the flaps there to fold into the hole around the valve stem
Note, patching a tube hear the valve stem is challenging.  Consider buffing the area of the hole really well, and allow the vulcanising fluid to set for 10 minutes before applying the patch, with pressure.   If the tube doesn't test okay, then just replace it.   Tubes are consumables too.


The best fix is new rim tape, which is not expensive, and the newer sorts don't stretch much around the valve hole.  You might still need a new tube.