The 23-year-old forward collided with an advertising board during the National League South match against Dulwich Hamlet at Twerton Park on November 9.
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And he is now looking at a 'long road to recovery' as he thanked football fans for their reaction to his injury.
In a statement on his club's website, Fletcher said: "Thank you all so much for your kindness, generosity and messages of good will that you have sent to me through what has been the most challenging period of my life.
"I am now off the intensive care unit and continuing my recovery on the neurosurgery ward assisted by the wonderful staff and nurses here.
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"I want to say a special thank you to all those who have been looking after me and my family and to everyone who has contributed to the go fund me page which will help me get back to doing what I love to do as soon as possible.
"It will be a long road to recovery but I will draw on all of the love and support that everyone has shown, every step of the way.
"Look forward to seeing you all in the future but in the meantime, up the Romans."
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Fletcher's family and fiance added: "We are all very relieved and so happy that Alex is now out of intensive care and heading in the right direction.
"We echo his words in thanking everyone who has shown so much love, good will and support towards us all and are convinced that this has helped in his recovery immensely."