First person to fill up unconvincing message (5)
I believe the answer is:
'message' is the definition.
(email is a type of message)
'first person to fill up unconvincing' is the wordplay.
'first person' becomes 'I' (first-person pronoun).
'to fill' means one lot of letters goes inside another.
'up' is a reversal indicator (in down clue: letters go upwards).
'unconvincing' becomes 'lame' (I've seen this in another clue).
'lame' written backwards gives 'emal'.
'i' inserted into 'emal' is 'EMAIL'.
(Other definitions for email that I've seen before include "Digital message" , "Message sent via computer" , "Electronic communication" , "Electronic message" , "Spam perhaps" .)