Why is the following sentence correct?

Question

The sentence I have is:

A lifetime friend and relative, my neighbour was often interested in the same subjects that I.

I would 'correct it' by replacing the last part with that I'm interested in

however, the book that I have states that it is correct as it is. Could someone explain?

Answer 1

It is not correct. It would be correct with as in place of that.

Answer 2

I would like to rephrase the sentence to

My neighbour, a lifetime friend and relative, was as interested in the same subjects as I am.