Thanks for posting your question in the Microsoft Q&A forum.
Moving the BMC FootPrints application server to an Azure VM should be relatively straightforward, similar to moving it to any other server. However, you'll need to ensure that the Azure VM meets the system requirements for BMC FootPrints Service Core.
Ensure that the connection string in the application is updated to point to the new Azure SQL Managed Instance. the problems with Java database calls could be related to JDBC driver compatibility. Ensure you're using the latest JDBC driver compatible with Azure SQL Managed Instance.
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