Depends on how the integration is setup. If its using his email/password it may break. If using TBA, then its a little trickier. You'd need to remove the integration token and recreate it and then use that info in the integration. IMO best practice would be to have a single user (employee) that isn't tangible and let that be your integration user so situations like this don't occur.
(also, if the person left the company, i'd do this ASAP as its a security risk to your company depending on intentions and is just an easy thing to control)