Yes you do. There are potentially fines for not notifying a change in circumstances, also remember it’s the entity not the business that’s registered so if you’re a partnership but registered as a sole proprietor then any fines, assessments, penalties will just be yours and yours alone.
Anyway to register you’ll need to fill out a VAT 1 (Registration application) with the partnership details, and if you want to keep the same VAT number (if it’s the same business continuing rather) you’ll also need to complete the VAT 68.
If you do transfer the number then it’s basically both of you agreeing that anything under the old sole proprietor can affect the new partnership i.e. if HMRC visit you and find that there was money that should have been declared whilst a sole prop then the partnership will need to pay it. So sometimes it’s best to get a new number when you change entity, so that “what happens in vegas, stays in vegas” as they say.
Look here for more info: https://www.gov.uk/government/publications/vat-request-for-transfer-of-a-registration-number-vat68