I want to use the B2BMA Integration User as my Account Engagement Connector User

Do not set the v1 Account Engagement Connector User as the B2BMA Integration User or attempt to edit it in any way. 

In v1 environments, The B2BMA Integration User exists to facilitate the flow of data between Salesforce and Account Engagement for several of the new releases and beta features like Connected Campaigns, Engagement History, or the Account Engagement Lightning App. The B2BMA Integration User is not suitable to be used as the v1 connector user because it cannot be edited and does not have login credentials for Salesforce. 

For more information on the B2BMA Integration User please see this article.

If you have a v1 connector and would like to upgrade to v2, you can refer to the instructions found in this article.