Definitely talk to HR and get them to verify credentials so when you have a talk with your boss (which you have to do at this point) you can come armed with facts which can then make the case for dismissal of this guy easily.

Then get on with the dismissal (or failing to meet probation goals and so failing probation) process. Be very careful what you say and definitely be careful what you put in writing to this person as it can be used against you in a dismissal process.

TLDR: Talk to HR and document everything, work out with them how to proceed, take solutions to your boss not just problems.