Paypal claim definitely best for the £500, as you say.It seems then that the payment went to the company that went into administration almost exactly two years ago, so a PayPal claim is the best course now.
.
The thing is that Moisson says he bought the bike a year before January 2015, so January 2014, then. The company actually went into administration in March 2012 and came out of administration in March 2013 and entered liquidation, thus ceasing to trade. There is no way Urbanmover.com Ltd could have sold Moisson the bike in January 2014 (and even if it were January 2013, he would not have dealt with Keith Chamberlain I believe, but instead the administrator, who I believe would have been obliged to inform Moisson that the company was in administration and might not be able to fulfil its commitments). It had to be Urban Mover Eco Ltd he dealt with (there is no other entity which Keith is director of).
The reason this is important is because Urban Mover Eco Ltd is still liable to Moisson for the bike having failed. Moisson should not have to pay for a new battery so long as he has not abused it. He should be provided with a repair, replacement, or part-refund (at the discretion of the retailer) - provided he paid good money for the bike. That (reasonable durability) is what Urban Mover Eco Ltd have agreed, it's the basis of his contract with it, and as an agreement is binding on the company.
I would point out that Keith Chamberlain is the company director for a school with £23m total assets, see here http://www.endole.co.uk/profile/2246250/keith-chamberlain so if Moisson doesn't hear from Keith he could always threaten to email the Chair of Governors at the school to ask for Keith's contact details...