O'Connor says Cole, who had the kidney transplant surgery on May 18, is "doing quite well under the circumstances."
The 59-year-old singer underwent the operation immediately after learning that a donor organ had become available.
The daughter of Nat King Cole had been receiving dialysis three times a week since September. But she still continued to perform in support of her latest album, the Grammy-winning "Still Unforgettable."
Cole postponed her summer tour, which was scheduled to begin June 5, so she can recover.
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