October 21, 2015 08:20 AM

Khloé Kardashian remains by Lamar Odom‘s side as he continues to receive treatment after being hospitalized Oct. 13.

The reality star, 31, was spotted accompanying her ex Odom as he was transported via medical helicopter on Monday from Sunrise Hospital in Las Vegas to Cedars-Sinai Medical Center in Los Angeles, where he remains in the intensive care unit.

A source confirmed to PEOPLE that the former NBA star had been moved Monday night.

“Khloé wants Lamar to get the best medical treatment possible,” another source told PEOPLE of the reasoning behind the move less than week after Odom, 35, was found unconscious last Tuesday in a Nevada brothel and just three days after he woke up this past Friday.

A Cedars-Sinai source also told PEOPLE the hospital is well-suited to take care of Odom: “For someone with heart problems, there is really no better cardiology team in the country than the Cedars team,” the source said. “Cedars has put together the best team possible.”

Kardashian – who has not left Odom’s side – has been making medical decisions for Odom since the pair’s divorce has not yet been finalized.

The Keeping Up with the Kardashians star wrote on her website Tuesday to thank both Odom’s and her fans as well as the team at Sunrise for helping them both through an “incredibly difficult” week.

“You can never be prepared for an experience like this, but without the outpouring of love and endless prayers that Lamar has received and the strength I was given from my loved ones, it would have been difficult to endure,” she wrote. “Thank you for your continued support. God is great!!!”

Odom’s aunt JaNean Mercer also issued a statement to PEOPLE about her nephew’s ongoing recovery.

“As Lamar begins a new chapter in his road to recovery, PLEASE continue to uplift him and the family in prayer. He continues to make miraculous progress, taking a few steps in Los Angeles. We couldn’t be more overjoyed!” she said in the statement. “We realize Lamar’s continued improvement will not be easy, however his unrelenting strength and faith in GOD will pull him through.”

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