Yes, you can.
If Purchased Mutual Funds in Demat mode: the process is simple, ask your existing broker to give you a DIS slip. In DIS Mention the units you have to transfer, mention your Fyers Demat account number, and submit it back to the broker. Usually, within 24 hours the units get transferred.
If purchased Mutual Funds in Non-Demat mode: In this case, you will have to dematerialize your mutual fund investments. Once dematerialized, it will start showing up in your Demat
To know more about Direct and Regular Mutual Fund Click here139.
Note: If the Mutual funds are in the Lock-in period, then you will not be able to transfer the units.