Yuk.
I don't know the ramifications of having the hot tub and pool exchning water, but
With my outdoor AGP, for algie, I use an algicide (the black aglicide, can't remember the name, but a dealer will know it). Scrub the sides, and for good measure, he could replace the sand in the filter. ($30)
Clean the Hot tub filter and super chlorinate.
If this doens't do it, I think he's looking at a complete water change out.