Unless there is gross pus or a draining sinus, our approach for an infected arthroplasty is a single stage revision to an impaction allografted hemiarthroplasty, see this link.
Here’s a case example

He returned to his favorite sport of swimming as shown below
After years of successful function he experienced the unexplained onset of pain and stiffness with a drop in his Simple Test score from 12/12 to 3/12.

He had a single stage revision with prosthesis exchange using impaction allograft followed by 6 weeks of IV Ceftriaxone and 6 months of PO Doxycyline.

He returned to swimming and now three years after his single stage revision his shoulder continues to function well with a Simple Test Score of 11/12