Should I notify my employer?
If you have some reason for maliciously trying to sabotage his new job you could pass on hearsay or even find proof and hand that in.
In theory though the employer should already be aware or they didn't do their homework properly. People do get hired despite being fired elsewhere for fraud, in some locales I've seen whole careers where a person has been forced out of multiple jobs for outright theft and still got another job, even in finance positions.
Depending on the position, your role, and locale you have no ethical or professional responsibility to do anything about this. You're obviously not part of the hiring process.