Can rate per hour be changed

My Sister has been working p/t 3 yrs in a permanent job for 13E an hour boss wants her to go F/T and has hinted that she might have to work for less per hour when F/T. If anything I thought she should look for more cash due to having more duties and reponsibilty .Her contract does state that she would at some point have to go full time if required which she is glad to do.Boss was trying to say something along the lines of p/t workers sometimes get paid more per hour than full. I think he is chancing his arm, Does anyone know what her rights are. It is not a union job. Thanks

Unfortunately a check out clerk for example may get promoted to say a junior manager. The promotion may come with a fixed salary no o/t and increased responsibilities duties. As a junior the wage could well be less than what the clerk may get on an average year allowing for o/t etc.
When I started my career i was on well less than the hourly rate labourers would get and no ot etc as above. Its just the way it is when starting as a professional in most industries it seems.....
I dont know does this scenario compare closely to what you query though.

if her boss values her as an employee, he is not going to cut her rate of pay. She should tell him when the issue is raised that she had actually hoped for an increase as the change is not only hours but also seems to be a promotion given the additional responsibility etc.

Even though it is not a union job, does the employer have published pay scales that it is trying to conform to?