AWS Database Migration Service (AWS DMS) is a cloud service that makes it possible to migrate relational databases, data warehouses, NoSQL databases, and other types of data stores to AWS quickly, securely, and with minimal downtime and zero data loss1. AWS DMS supports migration between 20-plus database and analytics engines, such as Microsoft SQL Server to Amazon RDS for SQL Server2. AWS DMS takes over many of the difficult or tedious tasks involved in a migration project, such as capacity analysis, hardware and software procurement, installation and administration, testing and debugging, and ongoing replication and monitoring1. AWS DMS is a cost-effective solution, as you only pay for the compute resources and additional log storage used during the migration process2. AWS DMS is the best solution for the company to migrate the financial transaction data from the on-premises Microsoft SQL Server database to AWS, as it meets the requirements of minimal downtime, zero data loss, and low cost.

Option A is not the best solution, as AWS Lambda is a serverless compute service that lets you run code without provisioning or managing servers, but it does not provide any built-in features for database migration. You would have to write your own code to extract, transform, and load the data from the source to the target, which would increase the operational overhead and complexity.

Option C is not the best solution, as AWS Direct Connect is a service that establishes a dedicated network connection from your premises to AWS, but it does not provide any built-in features for database migration. You would still need to use another service or tool to perform the actual data transfer, which would increase the cost and complexity.

Option D is not the best solution, as AWS DataSync is a service that makes it easy to transfer data between on-premises storage systems and AWS storage services, such as Amazon S3, Amazon EFS, and Amazon FSx for Windows File Server, but it does not support Amazon RDS for SQL Server as a target. You would have to use another service or tool to migrate the data from Amazon S3 to Amazon RDS for SQL Server, which would increase the latency and complexity. References:

Database Migration - AWS Database Migration Service - AWS

What is AWS Database Migration Service?

AWS Database Migration Service Documentation

AWS Certified Data Engineer - Associate DEA-C01 Complete Study Guide