Dear Matthew, I would like to wish you Happy Birthday and I would like to thank you for inviting me to your party next week. I will definitely be there and I look forward to…

Вот короткая неформальная версия на английском:

Hey Matthew! Happy birthday, and thanks for the invite to your party next week. I’ll definitely be there—can’t wait to see you and your family. Cheers, Paul

Если хочешь ещё короче, можно убрать часть про семью:

Hey Matthew! Happy birthday, and thanks for the invite. I’ll definitely be there. Cheers, Paul