infromal letter

Hello,
Could you please look over my letter/email and correct it, or tell me some suggestions.

I had to write an email(informal letter) to a friend inviting him/her to go either a concert or a film with me. "Give details of the place and time and say who else is coming and where you could go afterward. (120-150 words, at best 160)"

And here is the email:

Dear Denisa,

Many thanks for your letter - it was really nice to hear from you again. I'm sorry I haven't written for ages, but I've been busy preparing for my semestrial test papers. I was so glad when you told me that now you're fully recovered.

You remember I told you in my last letter that I was going to buy tickets for Rihanna's concert. Well, I did it, but I have two tickets and guess what: one is for you. I know Rihanna's your favorite singer so you can't say no to my invitation.

Anyway, the concert will be hold in the National Arena Bucharest, on January 18, in the same day you were born: So Happy Birthday, my dear friend! We're going by train and it'll be a weekend-trip. Aferwards we could go to the hotel Rihanna's staying to get an autograph. Don't hesitate to write me if you have queries.

See you next month.

Love,
Alice