Is this sentence correct?

No.

A better sentence would be: I was also invited to write a book chapter on understanding diversity and empowering students from ''somewhere'' to overcome their inclusivity challenges.

An even better sentence, in my opinion, would be the following:
I was also invited to write a book chapter on understanding diversity and how to empower students from ''somewhere'' to overcome their challenges to being and feeling included in their new country.


The sentence in blue is correct and closer to your original sentence. The sentence in red is also correct, but is better because it avoids an overly technical term, (inclusivity), which is better explained in plain language.

Either the blue or the red sentence can be used.

The last part isn't grammatical. As a phrase it's "inclusivity challenges." Or with a preposition, e.g. "challenges of inclusivity," "challenges concerning inclusivity," "challenges regarding inclusivity," etc.

I'd change "somewhere" to "somewhere else."

I was also invited to write a book chapter about understanding diversity and empowering students from ''somewhere'' to challenge inclusivity.