[AmE - not a teacher]
I'm not sure I can help you fix your sentences, but I can say that in the US, it's common to wish someone a "happy belated birthday".
I forgot my brithday.my friend wished me on that day.....(change this in to simple sentence).
Having forgot my birthday, my friend wished me. (or)
My friend congradulated me on my forgotten birthday.
Is this answer correct?
[AmE - not a teacher]
I'm not sure I can help you fix your sentences, but I can say that in the US, it's common to wish someone a "happy belated birthday".