How To Use Transactional Replication Across Internet?

I am currently experiencing issues with attempting to create a snapshot transaction replication across two servers on different machines that are not on a domain at all.

Server A - Distributor:
Computer Name: WIN-91KB167NSAK
Operating System  - Windows Server 2008
SQL Server - 2008
SSMS - 2012
Firewall off
All SQL server services running.

Server B - Subscriber:
Computer Name: TEST-2012
Operating System  - Windows Server 2012
SQL Server - 2012
SSMS - 2012
Firewall off
All SQL server services running.

I originally began by following this guide by Microsoft for creating transactional replication across two SQL Servers.

Everything was going smoothly until I reached the point of viewing the Synchronization Status, since then it has been a nightmare of attempting to follow breadcrumbs to try and get around the issue.

The latest solution I attempted was to connect through SQL Authentication for each step of the transaction login requirements, this fell upon

Date		05/08/2014 13:05:25
Log		Job History (WIN-91KB167NSAK-Northwind-Northweeend-TEST-2012-43)

Step ID		2
Server		WIN-91KB167NSAK
Job Name		WIN-91KB167NSAK-Northwind-Northweeend-TEST-2012-43
Step Name		Run agent.
Duration		01:21:15
Sql Severity	0
Sql Message ID	0
Operator Emailed	
Operator Net sent	
Operator Paged	
Retries Attempted	0

2014-08-05 13:26:32.789 Copyright (c) 2008 Microsoft Corporation
2014-08-05 13:26:32.789 Microsoft SQL Server Replication Agent: distrib
2014-08-05 13:26:32.789 
2014-08-05 13:26:32.789 The timestamps prepended to the output lines are expressed in terms of UTC time.
2014-08-05 13:26:32.789 User-specified agent parameter values:
			-Subscriber TEST-2012
			-SubscriberDB Northwind
			-Publisher WIN-91KB167NSAK
			-Distributor WIN-91KB167NSAK
			-DistributorSecurityMode 1
			-Publication Northweeend
			-PublisherDB Northwind
			-XJOBID 0xC58461878BB77D46AF089EBA55573246
			-XJOBNAME WIN-91KB167NSAK-Northwind-Northweeend-TEST-2012-43
			-XSUBSYSTEM Distribution
			-XCancelEventHandle 00000000000006B8
			-XParentProcessHandle 00000000000006C4
2014-08-05 13:26:32.789 Startup Delay: 7862 (msecs)
2014-08-05 13:26:40.664 Connecting to Distributor 'WIN-91KB167NSAK'
2014-08-05 13:26:40.664 Parameter values obtained from agent profile:
			-bcpbatchsize 2147473647
			-commitbatchsize 100
			-commitbatchthreshold 1000
			-historyverboselevel 1
			-keepalivemessageinterval 300
			-logintimeout 15
			-maxbcpthreads 1
			-maxdeliveredtransactions 0
			-pollinginterval 5000
			-querytimeout 1800
			-transactionsperhistory 100
2014-08-05 13:26:40.664 Connecting to Subscriber 'TEST-2012'
2014-08-05 13:26:40.696 Agent message code 20084. The process could not connect to Subscriber 'TEST-2012'.
2014-08-05 13:26:40.696 Category:NULL
Source:  Microsoft SQL Server Native Client 10.0
Number:  18456
Message: Login failed for user 'NT AUTHORITY\ANONYMOUS LOGON'.

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I have followed this to try and get a better understanding of the situation but the section I needed most if less than helpful and quite vague.

What would be the best solution to this problem, or is it likely just something stupid that I've overlooked in the process?

At this point the issue has become a net of complication for me so I may have overlooked important information to report, if any more details are required please ask.

Thanks for your time with helping on this issue.
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Eugene ZCommented:
as per the MS link "4.Request a SQL Server login account to be created on the Subscriber with sufficient permissions in the Subscriber database"

or just as test (if it is ok for your environment)  you can grant 'NT AUTHORITY\ANONYMOUS LOGON' sql server access on 'TEST-2012'

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PsychotextAuthor Commented:
Apologies for the very late reply, work required me to move on other items on my list and I'm now just re-visiting this.

The problem with number ""4.Request a SQL Server login account to be created on the Subscriber with sufficient permissions in the Subscriber database"

Is that it falls under the category
"Example 1: The Subscriber Has Schema and Data, and the Initial Snapshot Is Not Necessary."

Where in reality the solution I'm attempting to reach requires the initial snapshot. Which looks quite a bit more convoluted for the solutions applicable.
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Microsoft SQL Server 2008

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