The 22-year-old made two appearances for the League Two club during his month with the Cumbrians but is still waiting for his first team debut at Upton Park.
"Raphael enjoyed his time here and we enjoyed having him here with us," said Carlisle goalkeeper coach Tony Caig.
"I know he gained a lot from being with the first team and he showed a desire and determination from day one to learn, work hard and improve.
"If he takes that attitude with him going forward he will not go too far wrong."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!