Hey there,

What i would normally do is this;

Lets say the total project is $1500. 50% paid upfront, 50% at the end (but not even there yet).

10 other tasks were added to the project whilst adding content etc, new work... out of scope. This work should be either quoted for or set to an hourly rate, so you just charge for the extra time spent.

What I would do is send an invoice for the full remaining amount. Then include 'addition fees' to the invoice as per extra work - out of scope time spent on the project.

The email to them however, could be worded something like this...

Hello 'client name', Please find attached, the invoice for the final half of the project and additional work that was requested and completed. Due to the prolonged delay in getting this project completed on the estimated date, (I or We) are requesting for the final half to be paid in order to continue our work and finalise this project for you. If you have any questions please do not hesitate to reply via email or give us a call on 'number'. Kind regards, Name here

Hope that helps. Peace!