There are 2 ways to hold mutual funds. One in the demat form and another in physical (rematerialized) format. The method of transfer will vary depending on the form that your mutual funds are stored in.
Please follow the steps mentioned in here since transferring of Mutual fund in demat form is done in the same way.
Since the mutual fund are handled by the fund house, you don’t need to ‘transfer the fund’. To see the funds in the platform of your choice, you need to
Stop the SIP if you have any in your existing platform
Go to the platform of your choice and select import folio
You will then be taken to the CAMS / KFintech site where you need to enter the requested details
You will receive a CAS (Consolidated account Statement) in your email shortly
Depending on the platform and the access permission given, you will either have to forward the mail to the mail ID specified by the platform or they will automatically fetch it from your email.
You now can select the existing folio for SIP or lumpsum transaction