Co-worker/subordinate problem

Co-worker applied to a role in my department. I’m the most senior in this department. Co-worker was given the role, but has to split time with this role and the role that person is leaving until they get a new person to fill that role and is settled. Co-worker started the role 7 weeks ago, but had a week off for vacation. Over 6 weeks, the last 2 was spent on that person focusing on the previous role to train the new person. Come to find out the new person quit in 3 days. So co-worker only had to focus on that previous role. So in the other 4 weeks, and the last two weeks the co-worker promised that time will be given to learn and practice the new role they were given, so in the other 4 weeks….. multiple sessions via video conference were held. Many notes were taken, examples given, SOPs given. It was my hope that the co-worker/subordinate would have been proactive in going to the study material, video recordings of the conferences, SOPs, to have at least the Basics. Today we met, and basics were not met. I had to sit there re-teaching most of it. They didn’t even attempt to pull up their notes. They kept asking for hints. What do I do? I already lost my cool today over the conference call. I did the same when I at week 5 that person was supposed to submit a project I assigned them earlier that week, but didn’t do it, putting it off by a couple days, and then when I said to get on the video conference so I can see them work the project, they didn’t know how even if they had weeks of notes, examples, recordings of sessions, and SOPs. Now I was told my co-worker has until the end of September until they get assigned 100% to my department, and that person promised to block of time each day to work and learn job, October / November is supposed to be busy season. What if they aren’t up to speed on everything? What do I do? Ask management to transfer that person to another department? “PIP” them? Or let them flail around and I pick up the slack?