This could be a tricky one if there is likely to be a conflict between you and your teacher and I’d hate to be the cause of that. The two possiblities are: In spite of the fact that … or Despite the fact that … Another way of saying this is: Despite his illness - this sounds less complicated.
However, a little more on the original post:
Since ‘despite’ is ‘in spite of’, ‘despite [color=red]of’ would be ‘in spite of [color=red]of’ which is obviously redundant.