SQL Server log shipping: How to give SQL Agent the needed rights to remote share?
Create a service account in your Active Directory or as a local account on the primary server. Add that account to the folder's security permissions with change and read permissions.

http://www.mssqltips.com/sqlservertip/2562/sql-server-log-shipping-to-a-different-domain-or-workgroup/

The service startup account defines the Microsoft Windows account in which SQL Server Agent runs and its network permissions. SQL Server Agent runs as a specified user account. You select an account for the SQL Server Agent service by using SQL Server Configuration Manager.

https://msdn.microsoft.com/en-us/library/ms191543.aspx

To set the Service Startup Account for SQL Server Agent:


In Registered Servers, click the plus sign to expand Database
Engine.
Click the plus sign to expand the Local Server Groups folder.
Right-click the server instance where you want set up the Service
Startup Account, and select SQL Server Configuration Manager….
In the User Account Control dialog box, click Yes.
In SQL Server Configuration Manager, in the console pane, select SQL
Server Services.
In the details pane, right-click SQL Server Agent (server_name),
where server_name is the name of the SQL Server Agent instance for
which you want to change the service startup account, and
select Properties.
In the SQL Server Agent (server_name)Properties dialog box, in
the Log On tab, select one of the following options underLog on as.


https://msdn.microsoft.com/en-us/library/ms186264.aspx#SSMSProcedure



You must grant read permissions on this network share to the proxy account under which the copy job will run at the secondary server instance.

By default, this is the SQLServerAgent service account of the secondary server instance, but an administrator can choose another proxy account for the job.

Network path to the download folder