The Algerian was left in limbo late on deadline day when a £15million deal to take him to France fell through unexpectedly.
Benrahma had spent much of Thursday undergoing a medical in London and finalising the move to France, but the clubs were unable to complete the deal, leaving Lyon furious.
The Ligue 1 club had planned for Benrahma to sign his contract live on television but things quickly turned sour despite Lyon having registered all relevant details on FIFA's Transfer Management System (TMS) by 10.30pm Thursday night.
Lyon later accused the Hammers of botching the paperwork and released a strongly-worded statement saying West Ham had shown a 'deep lack of respect' before describing the club's conduct as incomprehensible behaviour.
The seven-time French champions took the case to FIFA who opened an immediate investigation into why the Hammers were unable to complete deadline day deals for both Benrahma and Pablo Fornals who was set for a £6.8m switch to Real Betis.
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World football's governing body have cleared the way for Benrahma to join Lyon, as revealed by the club's CEO Laurent Prud'homme during a press conference on Friday.
"I have just received a text from FIFA," he told reporters. "They have accepted the TMS certificate for Benrahma's transfer. It happened as we speak. Our efforts bear fruit."
Whilst things appear to be moving in the right direction for the winger, there are still some administrative tasks left to do before the deal can be finalised.
"Now the FA must send the International Transfer Certificate to France," talkSPORT football reporter Ben Jacobs clarified.
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"FIFA deemed the 'engager' [Lyon] followed protocol and inputted information correctly, and usually when this is the case a transfer can be salvaged."
Lyon's American owner John Textor also told the press conference: "The Benrahma story looks like it's going to be an ongoing story for, I don't know if it will be several hours or a couple of days."
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Meanwhile, LaLiga side Betis still hold hopes of tying up a deal for Fornals due to 'a computer problem' on West Ham's side being the reason behind the hold up.
"Let's hope it can be fixed," the Spanish club's CEO Ramon Alarcon said on Friday morning.
"The thing about Pablo Fornals happened at the last minute. There has been a computer incident, we have worked on it to be able to justify it. Betis has delivered the documents in a timely manner. West Ham seems to have had a problem with their computer tools. It has not only been in the case of Betis, but also in other cases.
"We hope it will be resolved in the coming days. We are working on it and we are optimistic, although in these things we have to be cautious."