Explanation
One benefit of creating user stories that the business analyst can share with the executive sponsor is that it saves time when prioritizing and implementing functionality. User stories are short and simple descriptions of a feature or functionality from the perspective of an end user or customer. User stories help to capture the value and benefits of a solution, rather than the technical details or specifications. User stories also help to facilitate communication and collaboration among stakeholders, developers, and testers. User stories can save time when prioritizing and implementing functionality because they can be easily ranked or ordered based on their importance, urgency, dependency, or impact. User stories can also save time when implementing functionality because they can be easily translated into development tasks, acceptance criteria, and test cases.
References: https://trailhead.salesforce.com/content/learn/modules/user-story-creation/write-user-stories

Explanation
The best way for a business analyst to gain the end users' cooperation is to identify key stakeholders and develop relationships with them as a trusted advisor; involve stakeholders and end users in the design of the new solution; and act as a liasion between business and technical teams. This will help them understand their needs and expectations, demonstrate value and benefits, and facilitate communication and feedback.
Responding to end users with empathy and accommodate their needs; translating the end users' needs into technical requirements; and delivering the project to the developers to implement the solution may be too reactive or passive without addressing the root causes of resistance or ensuring alignment. Using an assertive influencing style; demonstrating authority and expertise; outlining the project objectives; and making sure end users know that the decision has been made and the time to make changes has passed may be too aggressive or authoritative without building trust or rapport. References:
https://trailhead.salesforce.com/content/learn/modules/salesforce-business-analyst-certification-prep/collaboratio

This answer suggests researching third-party apps on the AppExchange as the next thing that the BA should do after a sales manager expresses frustration that the sales team is failing to enter calls in Salesforce, and hopes to resolve the issue quickly and has limited time and budget to complete revamp existing tools and process.
The AppExchange is an online marketplace where customers can find, try, buy, and install apps that extend the functionality of Salesforce. Researching third-party apps on the AppExchange can help the BA to find a possible solution that can address the issue of entering calls in Salesforce without requiring a lot of time, budget, or customization. Researching third-party apps on the AppExchange can also help the BA to compare different features, prices, ratings, and reviews of various apps that can meet the sales manager's needs and expectations. References:
https://trailhead.salesforce.com/en/content/learn/modules/salesforce-business-analyst-quick-look/use-stakeholder

The technique that the business analyst is using to understand UC's structure is stakeholder analysis.
Stakeholder analysis is a technique that involves identifying, analyzing, and engaging the individuals or groups who have an interest or influence in the project outcome, such as customers, users, sponsors, managers, team members, etc. Stakeholder analysis helps to understand the functions, interactions, and reporting relationships of each stakeholder group, as well as their needs, expectations, priorities, and concerns. Stakeholder analysis also helps to plan how to communicate, collaborate, and manage the stakeholders throughout the project lifecycle. References: https://trailhead.salesforce.com/content/learn
/modules/salesforce-business-analyst-certification-prep/stakeholder-management