As an HR manager, do you believe that the period of 3 months is enough as a probation period for managers and higher?

Not really - mainly if during that time the manager did not deal with any hiring, performance management, promotion or employee relations matters.
How would you assess this manager though? a360 assessment? a feedbak request to his reports and supervisor?

3 Months large.can Measurement period not exceed one month

3 months is fine as long as the management is honest and up front with the new employee concerning their work rate and performance.
This then ensures that there are no shocks when the employee is not kept on.
Management have to find time to give feed back to new recruits

Actually Probation period is a time span to judge the new hire.
Recruiters always try to get the best match for the position they are hiring.
but some times they do the mistakes.
Due to this the probation period is required.
I think90 days is enough to judge anyone.
You’ll usually know something's wrong in the first90 days.
The new person will be late completing projects, won't have the skills you might have thought, or won't seem to be putting in a lot of effort.
But most of the time you’ll find that the person just is not the right fit.
He does not really get along with – or “get” – the team.
It’s less what he does than how he does it.