The probationary constable is one of five officers from four forces faced with disciplinary action after investigations by the Independent Office for Police Conduct (IOPC) into social media messages about the killing.
The IOPC said the officer would face a misconduct meeting after allegedly sharing the meme. He was found to have been off duty at the time it was shared, though he later staffed a police cordon in the search for Ms Everard.
He does not face being sacked as he has not been charged with the more serious offence of gross misconduct.
Another probationary constable in the Met will be subject to a misconduct meeting for allegedly sharing the meme and “failing to challenge it”.
The IOPC also looked into allegations that seven officers from other forces breached standards by using the encrypted messaging app Signal to share information on the prosecution of Wayne Couzens, who was given a whole life sentence after pleading guilty to the kidnap, rape and murder of Ms Everard.
A Dorset Police officer, who was on secondment from the force, will face a gross misconduct hearing after being accused of posting details of the interview Couzens gave under caution, several months before the information could be made public.
The IOPC said the messages would have been a discredit to the police service and could have interfered with the course of justice if they had reached the public domain. The watchdog said it considered where there was a “legitimate policing purpose” in sharing the information.
The investigation indicated officers from other forces had “joined in the conversation, endorsing comments made by others and making unprofessional remarks about Couzens”, the IOPC said.
It said the actions of two others in the chat, from Sussex and Avon and Somerset forces, warranted misconduct meetings.
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The Sussex officer was cleared of misconduct at a meeting earlier this week but will undergo “reflective practice”. The Avon and Somerset officer still faces a meeting.
Sal Naseem, IOPC regional director, said: “The allegations involved in these two investigations, if proven, have the capacity to further undermine public confidence in policing.”
He also said the IOPC warned in April this year about “the unacceptable use of social media by officers based on a number of cases involving the posting of offensive and inappropriate material”.
Investigations continue into the conduct of five officers, three from the Met, one from Norfolk Constabulary and one from the Civil Nuclear Constabulary, and one former Met officer over allegations they sent misogynistic, racist and homophobic WhatsApp messages between March and October 2019.
The IOPC is also still looking into how Kent Police in 2015, and the Met this year, handled allegations of indecent exposure which have been linked to Couzens.
Additional reporting by PA