I would let the person go off and do the project by themself, but I wouldn't let them join another team and unfairly have 3 people to a team while others only have 2.
If the 1 person really is doing all the work, and the other team member isn't doing anything.. then the 1 person will be more then happy to go solo on the project. (Many group projects can be done solo anyways, it's just professors are pushed to have more group projects, so they shove out a project that can be done solo, but as a group project, just to tell their administrative oversight committee that they're meeting "group project requirements").
I had a group project in grad school where me and 2 other folks were in a team, but I was doing all the work. I told the prof mid-semester that since I was already doing all the work, I'd rather just do the group project all by myself and leave those other two folks hanging then keep doing all the work and letting them partake in the grade I was doing all the work for.
Prof was ok with that idea.
Because it wouldn't have me go join another team and throw off the balance.
Colleges these days seem to be inundated with group projects, because businesses have told colleges they're getting a bunch of grads that don't seem to do well in project teams. So, colleges have ramped up group projects to give students "experience" in group work.
But, college group projects are not like real work projects.
In work, there is incentive to do your job. If you don't, you get fired.
In college, there is often no incentive to work, because if you have at least 1 person in the team willing to do whatever it takes to make a good grade, and there's no punishment system in place to punish slackers, then slackers will just let the hard worker do all the work while slacking off.
So, if you haven't already got a peer review system in place, you need to put one in place. This lets each member of the group project grade the others. So, if one slacker is in the group, everyone else will give them an F. And, you have to decide how that works into the final project grade. EG: usually a professor will count the peer review as 50% of the project grade, and will then give their own grade to cover the other 50%. But, if a professor sees everyone giving a slacker an F, they'll probably skew their own grade to an F as well and average it out. But, the professor uses their 50% part of the grade to "Curve" the grade if needed. (Because colleges seem to yell at professors for flunking classes, even if the student is a slacking POS.)
The problem with peer review is when you end up with a group of slackers and 1 hard worker. The slackers can gang up on the hard worker and threaten them with a bad peer review score if they don't bust their hump. If that's the case, you'd hope the hard worker would tell the professor. But, it might not happen. So, you can still have 1 person doing all the hard work, but a bunch of slackers forcing them into the predicament.
I had one class where the professor let us fire a team member mid-semester AND do a peer review at end of semester... all to proactively take care of slackers. If the slacker was fired, they had to complete the project on their own and automatically got an F on the peer review. This lit a fire under a lot of students' rears, because nobody wanted to get fired.
Problem then was that the project could easily be done solo.. there wasn't enough work to go around. So, everyone in the group was worried about being fired and trying to jump on any work they could do.
(To handle the "demand" for group projects, a lot of professors are simply taking their class project, which they used to have students do individually, and just have them do it as a group now. So, you have projects that are pretty simple to do, and thus a hard worker can do it all, which just means slackers look at it and go "meh, I know one person can do that, so I'll just hang back until that person gets on it.")
Basically, college group projects are designed to promote slacking and reward it. Professors that think a student will magically rise up and show management skills by "whipping everyone into shape" are delusional unless they give the students a punishment mechanism by which to give their threats to the slackers some teeth.
The fact that your professor doesn't have anything like this in place yet is a bit alarming.
As a TA, I'd say let this person do the project by themselves (but not join the other group).. so they can cut the slacker loose... and also get with your professor to get a peer review system in place STAT.