The woman took a photo of her screen showing the friend request from Michael Lion but it didn't capture the whole screen.
Green denied sending any friend request to a Facebook account in the complainant's real name - but accepted that he sent a request to a "Nicole Elwood", but said he didn't know it was one of her aliases.
That account's profile picture was of the Grim Reaper and had nothing to indicate it was one of the woman's Facebook accounts, Judge Walker said.
It was also one of 252 friend requests Green sent at once.
"It appears ... Mr Green was in the habit of sending large numbers of friend requests, largely to people he did not know but whose names he had obtained from publications and names which were in the public domain," the judge said.
"These included female sports stars, cheerleaders, women listed on model agency sites."
After police seized Green's phone, they accessed his Facebook activity log but no direct friend request to the complainant was found.
The woman told the court the Facebook request had been sent to her personal profile and rejected the proposition it was sent to the Nicole Elwood account.
But Judge Walker said in his judgment which he delivered last month that he couldn't rely on that evidence because of the absence of the request in Green's activity log.
"The reasonable possibility is that the complainant is mistaken in that respect."
The judge said the evidence left him with a reasonable doubt as to whether Green sent the request to the complainant's account and "the charge must therefore be dismissed".
Green's defence lawyer, Sam Wimsett, said "obviously Glenn has a terrible record and has spent plenty of time in prison".
"But on this occasion he was adamant he was innocent and defended the case. In my view the evidence supported him and he was rightfully acquitted".
In 2015, Green was jailed after being found guilty of texting a woman he had stalked sporadically for 20 years after being released from prison for just a matter of days.
His criminal history of more than 20 years features more than 200 convictions, including 34 breaches of protection orders, seven counts of criminal harassment and six of perverting the course of justice.
Green - who also uses aliases Holden, Carlione, Colcord, Goldberg and Versace and Dallas Deangeles - is understood to suffer from erotomania: a type of delusion in which the affected person believes that another person, usually a stranger, high-status or famous person, is in love with them.