I can give a real life example of the procedure to change from the 'microlight' category to 'group A'.
I purchased a Jabiru UL-450 that was a 'microlight' and because I had a PPL I wanted it so I could log my hours.
Basically all I had to do was fill in the LAA form and send off £135. There were a couple of changes I had to do beforehand. The first one was that most of the placards in the aircraft had to be replaced as once in 'Group A', there is no minimum empty weight as there is in the 'microlight' category. On mine, I also had to have the flaps adjusted. I am not sure why that was required but I did have to have it done. I just got my LAA inspector to change the placards and do the flaps and he filled in a worksheet that went off to the LAA with the form and cheque.
I was told by the LAA that it would take about 4 weeks and that the aircraft was grounded until the process was complete.
Be aware that the LAA take ages to do anything other than normal permit renewals. It actually took them 9 weeks to complete it and the aircraft could not be flown during that time.
After that 9 weeks, I received a new permit and registration and the aircraft is now called a Jabiru SPL-450 and now I can log my hours.