I hope the relevant Form 13 relates to EPF only. Form 13 of EPF is meant for transferring the EPF balance of an employee when he leaves an establishment and joins another establishment where PF applies. It is to be forwarded through the present employer. In Form 13, there is no requirement of the previous employer's signature, but mention of the name and address of the previous employer, along with the previous account number, is required.
Regards,
Madhu.T.K