Can I continue investing in my Indian EPF after I leave a job in India and move abroad?

Contributions to the Employees' Provident Fund stop once you leave Indian employment, since EPF contributions come from an active Indian salary. Your existing balance keeps earning interest, but be aware that under EPF rules interest credited after the account becomes 'inoperative' or after you stop contributing can lose its tax-exempt status even in India. As a US tax resident, the annual EPF interest is generally taxable to you in the US, and the account is reportable on FBAR and Form 8938. Many returning-optional NRIs eventually withdraw the EPF balance once eligible and redeploy it. If the US-India totalization agreement existed it could help with social-security-type coordination, but no such agreement is currently in force, so EPF stands on its own.