On the Jacob_Archive database you need create an External Data Source that makes reference to the source database.
CREATE EXTERNAL DATA SOURCE RemoteReferenceData
Then create External Tables for all tables on the source database that you want to archive data.
CREATE EXTERNAL TABLE [dbo].[zipcode](
[zc_id] int NOT NULL,
[zc_cityname] nvarchar(256) NULL,
[zc_zipcode] nvarchar(20) NOT NULL,
[zc_country] nvarchar(5) NOT NULL
DATA_SOURCE = RemoteReferenceData
Then extract all the data you want from the remote table using an elastic query. You can create a stored procedure to extract the data you want to archive and put it on a table located on the Jacob_Archive database.
Once you have extracted the information you can run a stored procedure on the source table to remove the archived data. You can create an schedule task to perform/run both stored procedures using Azure Automation.