She was rushed to Princess Alexandra Hospital in Harlow, Essex after falling at home on March 6.
She spent three days in hospital, but sadly died of her injuries, with her husband by her side, Essex Live reported.
When her husband went to get his things, he discovered that two rings were missing.
The engagement and wedding rings were worth a total of £ 13,500.
The rings never left Ms Green’s hand during treatment and police now believe they were stolen.
PC Daniel Burns, of the Harlow Local Police Team, said: “These two rings are very special for the husband because they were both engagement and wedding rings and were bought for her in America.
“The combined total value of these two rings was $ 19,000, which equates to around £ 13,500.
“The husband is of course incredibly upset and upset by this. “
He added, “We are looking to speak to anyone who might have information on the whereabouts of these rings or if anyone has attempted to sell them. “
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If you have any information that might help officers with their investigations, you should call 101 and quote 42/78926/21.
Information may also be shared with the independent charity Crimestoppers anonymously on 0800 555 111 or https://crimestoppers-uk.org.