If your outgoing project leader is still around, speak to him about this. Ask for personal advice about what to do in this case where you carry the load for both you and this other worker.
It always helps if you state your problem as a company and customer issue as well as a personal issue.
For example, say "I am worried that Betty's poor performance on this project is going to make us late and annoy our users. I'm also worried that personally I am spending time trying to help Betty rather than do my own job. How can I deal with this situation in the best way for our users and our company?"
This project leader surely understands what's going on.Conversations are powerful: your act of asking for advice will help the project leader figure out how to act in your interest.
You could also say to Betty herself, for example, "You left this task only partially complete. How shall we work together to complete it?". For another example, you say "It would be helpful to us meeting our shared deadlines if you stayed away from social media web sites during the working day."
Notice that you're using your shared interest to motivate her. That will work better than saying "your laziness makes more work for me," even if it's true.
If you do speak to her, be aware that she is not going to immediately agree with you. She is going to deny that her work is not completed. She is going to say "It's none of your business that I spend time on Facebook." Do not argue with her when she denies these things. Just let her speak. When she's done, simply say, "I hope you'll think over what I have said. Thanks!"
When you intervene in bad behavior by confronting someone, it takes them a while to absorb your input. Everybody has a time constant. If you walk up to somebody who trusts you and truthfully say "you are wrong," some people will take an hour to agree with you. Some will take a day. Some will take a year. It is helpful to figure out how long the time constant is for each person you work closely with.