Which AWS services should the solutions architect use?

Explanations:

AWS Backup is a service for backing up data across AWS services and on-premises environments. It is not a file storage solution and doesn’t provide direct access to shared file storage for Linux servers.

AWS DataSync is used for transferring large amounts of data between on-premises storage and AWS. It does not provide file storage but is focused on data migration and synchronization.

AWS Snowball Edge is a physical device used for large-scale data migration and edge computing. It does not serve as a persistent file storage solution.

AWS Storage Gateway provides on-premises access to cloud-based storage. It offers file-based (NFS/SMB) storage through the File Gateway, which can be used for on-premises Linux servers and applications.

Amazon Elastic File System (EFS) provides scalable and fully managed NFS file storage in the cloud, which can be mounted on Linux servers on-premises via VPN, making it ideal for the scenario.