However, she still needs brain and spine surgery.
Morgan urged the hitmaker to acknowledge the family woes in an appeal made via the publication: "Your sister is dying and she's struggling and where are you? You think you are so fabulous, but you are a witch."
He said he has been by Alison's side during her health problems and flew from Italy, where he lives, to go see her, fearing she would die - but claims Mariah has never visited her in hospital.
He adds: "Thankfully, Alison had a miraculous recovery but now she needs brain and spinal surgery and will be going into hospital any day."
Morgan went on to insist that Mariah spends more on her beloved pets than she could easily fork out for her ailing sibling.
He adds: "She probably spends more on dog food than it would cost to make sure her sister gets properly cared for."
Despite Alison reaching out to her sister "over and over again", he said the pair of them never hear back.
Alison, a mother-of-four, became pregnant at 15 and turned to prostitution to fund a drugs habit.
She revealed she worked as a prostitute in New York to clothe and feed their family before Mariah found fame - and hasn't spoken to the star properly since having a huge argument in 1994.
After she was diagnosed with HIV, she then attempted to publish a tell-all book about her sister. The singer reportedly refuses to have her sister's name mentioned in her presence.
A few years, she spoke of how she longed to meet her niece and nephew Moroccan and Monroe - Mariah's four-year-old twins with ex-husband Nick Cannon.
Additionally, he claims he told his famous sister that his wife suffered a miscarriage, but didn't receive a response.
MailOnline has contacted a representative for Mariah for comment.
Last year, Morgan spoke out about his famous sister as he admitted he fears her drinking will kill her - and that he has never seen her sober.
"I can't say that I have ever been around her when she was sober, and that's very scary," he told the National Enquirer,
According to Morgan, Mariah has allegedly been a heavy drinker since suffering from mental health problems in 2001.
He revealed that he fears "she'll die like Whitney Houston" because she allegedly takes a combination of prescription pills.
"She does not have a support system, and she is not mentally capable," he said.
Now, she is heading down the aisle for a third time - after her seven-year marriage to Cannon ended last year.
Her first marriage to Sony Records boss Tommy Mottola, who discovered her when she was waitressing, ended in divorce in 1998.
But Morgan, who says he hasn't spoken to his famous sister in more than two years, isn't hopeful for an invite. The pair fell out after he tried to warn her against marrying Cannon.
He said he only found out about her latest engagement, to Australian businessman James Packer - worth $4 billion, according to Forbes - through social media.
Morgan says the money their sister needs is "small change" to Mariah and Packer, 48.
"Why isn't our millionaire sister and her billionaire fiancé helping out?"
- Daily Mail
