He can lop off the end of a spare USB cable (they multiply like rabbits around here), isolate and identify the pin-outs, and measure that way. My smaller muli-meter leads will fit a USB connector with no problem, so his should work if they are small. Measure both under load and un-loaded.

Things to check for on a system like that...1)check that the lithium ion battery has a full charge. That battery probably acts as a buffer to flatten out and regulate the voltage fluctuations of the peltier device due to heat variations.
2) make sure the voltage requirement of the device you are trying to power is below the stoves output capability. USB pin 1 (red wire) is +5 vdc. An iPhone battery is +3.7 vdc and wants to see that or more, regulated.

I was given a "Solar iPhone Charger" and gave up on the thing due to regulating issues. The phone charging scheme would shut itself down if the charge voltage was unstable. A buffer battery would have helped but it would have taken days to charge it with the dinky solar cell.

So, if your output is dropping below the device requirements or is unstable, and the device has a firmware controlled charging scheme, it might not charge. Top off that lithium ion batt to a full charge and see if that doesn't get her going.