Yes!!
Ok.
What should I write in the email (besides for attaching the invoice)?
Also, what do I do if he doesnât pay?
Since its only the first time your emailing your client I think you can just say see invoice for the final design. Feel free to send at your earliest convenience 
would love to know which one you ended up going with.
This kind of basic words⌠I honestly just email whatever comes to mind each time. I have had times where clients needed reminders to pay. Its normal
Thanks.
To clarify, I only sent him the initial design options. He didnât get back to me since.
so say, Hi please see attached invoice, let me know what changes you wantâŚ