The solution
Aside from recreating the signature via the Outlook Signature Editor or applying the VML picture implementation, you can configure Outlook 2013 to always embed all linked pictures (just like previous versions of Outlook) by setting the following Registry key.
Key: HKEY_CURRENT_USERSoftwareMicrosoftOffice15.0OutlookOptionsMail
Value type: REG_DWORD
Value name; Send Pictures With Document
Value: 1
Note: The value name contains spaces and capital letters; you must include these as well.