What should a solutions architect do to meet these requirements?

Explanations:

Amazon FSx is a managed file storage service, but it is not the best option for reducing costs when files are infrequently accessed after a few days. It is also less cost-effective compared to S3 for large files that are not accessed frequently.

Storing files locally on each EC2 instance does not provide shared access across the cluster, complicating data management and increasing costs due to lack of centralized storage. Additionally, it does not effectively address cost reduction as local storage on EC2 instances may be more expensive than using S3 or EFS IA.

Configuring a Lifecycle policy to move files to the EFS Infrequent Access (IA) storage class after 7 days is a cost-effective solution. It allows for reduced storage costs while still providing access to the files that are needed initially. EFS IA offers lower storage costs for files that are infrequently accessed.

While moving files to Amazon S3 can reduce costs significantly, rewriting the application to support mounting the S3 bucket may introduce complexities and performance issues, as S3 is not a file system. Additionally, this solution does not directly address the need for shared access among Linux servers.