1) Since it is a proprietary firm and it is proposed to change the ownership of firm from Husband to Wife, you can execute a simple conveyance deed transferring the business from Husband to wife and get it registered at sub-registrar office. The cost of registration of transfer of ownership will be about Rs3500-/- at Sub-Registrar office.
2) Also for change of ownership details for GST, You should change the ownership details by filing a GST registration amendment application has to be filed electronically. The existing GST registration certificate need not be cancelled.
3) All changes to GST registration information, the GST amendment application form GST REG-14 must be digitally signed by the applicant within 15 working days of change in any information.
4) After filing of the application, a GST officer has to verify and approve / disapprove it within 15 working days in the FORM GST REG-15. When approved, the amendment would be applicable from the date of the occurrence of the event warranting the amendment.
Hope this information is useful.