Something like the below would work.
Global
Triggers: onAfterUserRegistration, onAfterNewUser, onAfterUserUpdate, onAfterUpdateUser
Type: Field
User: Automatic
Access: Everybody
Action
Field: cb_subs_inv_first_name
Operator: Set
Value: [firstname]
Field: cb_subs_inv_last_name
Operator: Set
Value: [lastname]
Field: cb_subs_inv_address_street
Operator: Set
Value: [cb_address]
Basically keep adding field value changes for the cb_subs_inv fields then set them to whatever CB field value you want. This will allow registration and profile update to change those field values instead of being exclusively done in basket.