"Our family are grateful to the wonderful carers & nurses who helped us through the hardest of times. You left in autumn, your favourite time of year. Rest now my LOVE."
Kusumphorn's cause of death has not been disclosed.
"Jane, myself and our kids now all need to be together elsewhere over the coming days as we all say an unexpected goodbye to someone we love," Barnes posted on May 24.
"This decision was not taken lightly but we trust people will understand that at times like this, family really must come first."
The tragedy came shortly after Barnes lost his sister Linda in May.
"Thank you for all your messages of condolence for my beautiful sister Linda's passing," the singer wrote at the time. "This week has been tough and overwhelming. Your support is appreciated."
