2001 i30 Fuel level always says full

[asnorton44]

Hi,

I just bought a 2001 i30 and the fuel level gauge is stuck on full. When the car is turned off it goes down to E as it should. Because the needle moves is it likely the fuel level sending unit and not the instrument cluster?

Would this part probably fix it: ?
https://www.amazon.com/OES-Genuine-Send ... B00279LHG8

Any instructions out there on how to install?'

Thanks!