@Jorge Rodrigues Welcome to Microsoft Q&A Forum, Thanks for posting here!!
If the available network bandwidth (1 Gbps - 100 Gbps) is high on the Azure VM, you can use azcopy tools to copy the data across storage accounts within the same region which offers free data egress charges.
AzCopy - Use this command-line tool to easily copy data to and from Azure Blobs, Files, and Table storage with optimal performance. AzCopy supports concurrency and parallelism, and the ability to resume copy operations when interrupted.
There are also other tools such as Azure Storage REST APIs/SDKs, Azure Data Box family for online transfers, Azure Data Factory to move the data across storage accounts
You can also choose other data transfer solution based on network bandwidth availability which are discussed here: https://learn.microsoft.com/en-us/azure/storage/common/storage-choose-data-transfer-solution#selecting-a-data-transfer-solution
Hope this helps!
Kindly let us know if the above helps or you need further assistance on this issue
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