Existing Tenants want to move Friend in to Spare Room

Tenancy Types and Management

We have a Single Mum renting a 3 Bed property with her Daughter on an AST for £500pcm. They receive £450pcm LHA(2 Bed Allowance) towards this and Top Up the rest through support from the child's Dad.

The Tenant would like a Female Friend to move in to the spare room in the house to help out with the rent and Bills. The Friend is Unemployed so would also need to claim Housing benefit for the rent.

Do I need to issue a new room only AST to the Friend so she can claim the Housing Benefit, or just add an amendment to the original AST granting permission for her friend to live there. Then could the original Tenant claim for 3 bed housing allowance?

Any help or advice would be much appreciated. Thanks in advance.