Complex sentence: Beeston would oversee several different troupes in the Cockpit before his 1639 death, the last of which, Beeston's Boys, would continute in the theatre under the management of his son William (Thomson 225).
Split into simpler sentences: Beeston would oversee several different troupes in the Cockpit before his 1639 death. They would continue in the theatre under the management of his son William (Thomson 225).