The key requirements are shared file access, NFS protocol compatibility, and no application changes. Amazon Elastic File System (EFS) is a fully managed, scalable file system that natively supports the NFS protocol, making it an ideal drop-in replacement for on-premises shared file systems used by Linux applications.

Option C allows the existing web servers to mount the EFS file system using standard NFS mount commands, preserving application behavior and avoiding code changes. EFS is designed to be accessed concurrently by multiple EC2 instances across Availability Zones, providing high availability and elasticity without manual capacity management. This aligns well with typical web server architectures that rely on shared content or assets.

Option A and B use Amazon S3, which is an object storage service and does not support NFS semantics. Migrating to S3 would require application changes to use object-based APIs instead of file system operations. Option D uses Amazon FSx for Windows File Server, which supports SMB, not NFS, and is intended for Windows-based workloads.

Therefore, C is the correct solution because Amazon EFS provides NFS compatibility, shared access, high availability, and minimal operational overhead while requiring no changes to the existing Linux-based web server applications.