Cheat at falsely presenting a case (7)
I believe the answer is:
attache
'a case' is the definition.
(I know that attache is a type of briefcase)
'cheat at falsely' is the wordplay.
'falsely' indicates anagramming the letters.
'cheat'+'at'='cheatat'
'cheatat' anagrammed gives 'ATTACHE'.
'presenting' acts as a link.
(Other definitions for attache that I've seen before include "Member of ambassador's staff" , "Specialised envoy" , "Embassy official" , "Embassy worker" , "Connected to the French" .)