time off work writing up thesis

Hi guys,

my friend on HSMP was a part-time PhD student and had to take 4 months off work to write up their PhD thesis.

What, in your opinion, is a better way of presenting this to the HO:

a) put in 4 months of unemployment (without giving a reason; not mention the part-time PhD study at all)
or
b) state that the time off work was taken to write up the thesis.

If they go for variant a), should they provide any evidence that they were actively looking for jobs during those 4 months and if so, in what form should this evidence be presented?

Thanks for your advice!