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His smelling salts left the woman with tears running down her face.

Suzuki Forenza Wagon leaves much to be desired.

Hi, can I rephrase the second like,

Suzuki Forenza Wagon leaves back much to be desired. And based on the strong predicative correlation between them can I rephrase the first sentence like,

His smelling salts left the woman back with tears running down her face. Thank you.
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No, and no. "Leave behind" in only appropriate when "leave" refers to a physical departure -- if you go away, you might leave someone or something behind. In the first sentence, "leaves much to be desired" is an idiom that means "is greatly lacking" or "fails to mneet expectations." In the second sentence, "left" has a temporal, rather than a physical sense -- "after using the smelling salts, the woman had tears running down her face." "Behind" does not work in either of these examples.
Comments  
I'm also going to suggest these,

Suzuki Forenza Wagon leaves much to be desired behind. and

His smelling salts left the woman behind with tears running down her face.
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 khoff's reply was promoted to an answer.
Thanks, khoff.