First thing I would try is to connect the laptop to the router with an ethernet cable and then try the transfer. Incidentally, your method is OK (find the share then start the transfer). There is one other method but it's a bit of a hassle as it involves using a crossover cable to link the two PCs together direct but of course that means scrabbling round the back of the desktop and swapping cables around. Another option is something like this.
All the choices outlined above are simply ways of doing the transfer without using the wireless part of the router because I reckon that's where the problem lies.
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Do you know that we're all in line for succession to the throne? Really?
Well, if forty-eight million, two hundred thousand, seven hundred and one people died I'd be Queen.