Issue

New messages sent from an iPhone are received as plain text : all the body part, not just the signature.

Solution

With in the main signature you have an option on the Plain Text Version for 'Convert email to HTML and use HTML signature' this will perform a conversion on the initial email from an iPhone and convert it to HTML and have the signature that you are expecting. 

Please note that this will convert all plain text emails, if your Organisation has systems that generate plain text emails, please test this setting.