How can a boxer continue his work if he dislocated his elbow?

Can't. A boxer would have no power to his punch when his elbow dislocates and would lose as the ref would stop the fight. Find a cause and c if it can b fixed. If so do it, but do not return to boxing.
Depends On Injury. There are several types and degrees of elbow dislocations. How soon a boxer could return to full activity would depend on the injury and rehab. During rehab, there are activities in boxing that they will be able to do. They will be able to increase the level of activities as their rehab progress.