cable short

Please forgive my elementary question but I'm quite young and learning new DIY stuff every day. Found a plug in electric mower being given away free - think it's just got a faulty power cable. Tested cable resistance with multimeter by putting red probe on bottom left plug prong and black...

I bought a wall mounted electric radiator, however the cable exit on the right hand side, but my electric socket is on the left hand side. I opened the heater, but they have soldered the cable onto the heating element. So there is no way of removing the cable and replacing it with a longer...