The H2020 Annotated Model Grant Agreement, on p.504, details that both supervisor and fellow must give their version of events when asking for the amendment.
The Beneficiary Termination Report is submitted by the beneficiary whenever the institution terminates the grant agreement earlier than initially foreseen in the Grant agreement. It creates the situation when the institution needs somehow to report to the Research Executive Agency before the usual periodic reporting is required for the project. It can happen when the former Individual Fellowship host institution (X) terminates the grant agreement and the grant agreement is transferred to a new Individual Fellowship host institution (Y).
The institution X first and foremost needs to submit the financial statement (form C) for the period they were active on the project. The Beneficiary Termination Report is a supporting document (technical report) to that financial statement. Just like the usual Periodic Report is a supporting document to the periodic Financial Statement. In that sense it is the institution X that is responsible for its preparation, delivery and signature, not the hosted researcher.
Everything else works exactly the same as for any other periodic report, except that once the Report is approved by the Research Executive Agency, the institution X is obliged to transfer the remainder of the funds to the institution Y.
More information can be found at the “Report About Beneficiary Termination” section here.