[Support] A letter to the HR office... Please, could you check it?

I am writing a letter to my HR office regarding some days' holiday and I would like to check my writing before sending, please.

HR writing

As at you last day with us you are entitled to 6.5 days holiday. You have taken 9 days, and therefore we need recover 2.5 days holiday. This equates to a figure of £xxx.xx and this will be recovered in your final payslip.

My writing should be as below:

Further to my 9 days' holiday taken against the 6.5 days' holiday which I was entitled to take, I would like to inform you that I took the 22nd, 23rd and 24th of December against overtime worked within CompanyName and authorised by ManagerName. I worked for over 30 hours on overtime which means up to 4 days of holidays. Please, check with ManagerName about the authorization.

MANY THANKS FOR THE HELP