I believe that you should have requested your present HR to allow you to leave in two months, but HR likely rejected it. Then, you could ask for an additional month to join, explaining that the present organization's HR is urging you to stay for an extra month. If your future HR does not find this arrangement acceptable, you may need to decide whether to join an organization that lacks flexibility. Engaging in a conflict with your current HR could result in negative remarks being added to your service records, which could harm your career once again.
It's important to remember that HR does not hold decision-making authority within an organization. They can, however, advise management on policy flexibility. For instance, if the standard notice period is three months, it could potentially be reduced to two months. An HR professional who takes employee advocacy personally may not be the best fit for the role. It is essential for HR to have an understanding of employment laws, particularly regarding notice periods.
According to the Industrial Disputes Act, in order to terminate an employee, an employer must provide notice. However, the Act does not stipulate that an employee must give notice when leaving an employer.