INSERT INTO from two different server database

It sounds like you might need to create and query linked database servers in SQL Server

At the moment you’ve created a query that’s going between different databases using a 3 part name mydatabase.dbo.mytable but you need to go up a level and use a 4 part name myserver.mydatabase.dbo.mytable, see this post on four part naming for more info

edit
The four part naming for your existing query would be as shown below (which I suspect you may have already tried?), but this assumes you can “get to” the remote database with the four part name, you might need to edit your host file / register the server or otherwise identify where to find database.windows.net.

INSERT INTO [DATABASE.WINDOWS.NET].[basecampdev].[dbo].[invoice]
       ([InvoiceNumber]
       ,[TotalAmount]
       ,[IsActive]
       ,[CreatedBy]
       ,[UpdatedBy]
       ,[CreatedDate]
       ,[UpdatedDate]
       ,[Remarks])
SELECT [InvoiceNumber]
       ,[TotalAmount]
       ,[IsActive]
       ,[CreatedBy]
       ,[UpdatedBy]
       ,[CreatedDate]
       ,[UpdatedDate]
       ,[Remarks] FROM [BC1-PC].[testdabse].[dbo].[invoice]

If you can’t access the remote server then see if you can create a linked database server:

EXEC sp_addlinkedserver [database.windows.net];
GO
USE tempdb;
GO
CREATE SYNONYM MyInvoice FOR 
    [database.windows.net].basecampdev.dbo.invoice;
GO

Then you can just query against MyEmployee without needing the full four part name