Firstly, it's my understanding a Cat B must be given up to a registered dismantler, to ensure the frame's destroyed?
Anyhoot, you'll need to swap everything into the replacement frame and re-MOT it (assuming the replacement frame still carries a reg number, VIN plate & headstock stamp unmolested). Apply to DVLA for a new V5c in your name, with an engine number change, that should be it. However, DVLA may at any time request a single vehicle test if they have any reason to suspect iffy-ness