Negotiating a higher salary/ pay rise in new role

[Becauseimworthit79]

I've name changed for this but I'd like some advice about asking for a pay rise in a new role at the same place of employment, please.

I started a new role in January after being approached by one of the managers from another department, because he recognised I had the skills and experience for it. I had to apply and go through an interview as it was a grade above the one I was on but it was given as a range so I hoped that I would be able to negotiate a higher salary.

Got the offer letter to find they were going to start me on the lowest amount for it, but I have plenty of reasons why I think I should be on a higher amount and even discussed this with the head of department who also thought I would be on a higher point. Anyway, she advised me to put this in an email and she would take it to HR to put my case forward.

Has anyone had any experience of asking for a pay rise by letter and if so how do you start it off and was it successful?

Thank you in advance.