There are no such thing anymore as sicknotes unless its a self cert. The ones the doctors produce are “fit notes” which cover what the person is able to do and what they are not. If the first job has things in it which the doc is saying the person isn’t fit to do and the second job doesn’t then I can see how the person might be okay to do job one and not job two. I know of someone who had this issue working both jobs in a school. The first job entailed lifting heavy weights and the second job did not. The school were fine with this and understood, he carried on doing job b while being signed off in job a. Are the two jobs with the same employer?