What is the 35.9? Don't see how it can be Wh since 13x3166 = 41.2.
Maybe there is some accounting for thermal inefficiency or other losses?
Regardless, 3166mAh at 13V would be equivalent to just a 11,400mAh at 3.6V nominal. Really quite hard to believe this given the comments about the things size and weight, but...
Plenty of third party power banks should be able to provide a charge to the connected battery. The 25,600mAh Shargeek Storm 2 would be up to the job I'm sure, and if the regular battery provides 3 hours of use, then this would add a further 6+ hours on top.