Hi Debbie,
It looks like the last 3-monthly hormone injection was 14/1/19, so that will run out approx April 2019. Testosterone can start appearing at that point, but might take up to 18 months, and you're well within that when PSA starts rising. You expect PSA to rise when your testosterone comes back, because you still have a prostate, and the non-cancerous parts will survive and switch back on (including making PSA, one of the prostate's main jobs) in the presence of testosterone. So I would say what you're seeing is fully expected, as you suggest. Does the increase in PSA also correspond with a period when he noticed reversal of any HT side effects, such as regrowth of body hair or any others?