I hope you're fine
It was good to hear from you.
Thanks for your letter.
I'm writing to tell you/ to thank you..
I wonder if you remember..
As for my latest news..
I'm writing to ask you for help/advice
I'd be really grateful if you could..
If you've been wondering what I've been doing, here's the latest news.
I thought I'd write and give you the lates news.
You won't belive it but..
Guess what! I've just..
I'm sorry I haven't written for so long but....
Drop me a line soon! -napisz do mnie szybko