“Today I leave Grenada with a broken heart,” wrote Elizabeth “Liz” Waddell’s sister

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The family of Elizabeth “Liz” Waddell — the North Carolina woman who vanished while vacationing in Grenada — has made a difficult decision: They’re returning home.

“To everyone invested in Liz’s story: The family will travel home today, Friday, July 31,” wrote Cailen Waddell on a website dedicated to the search for his wife, Liz. “We have done what we can here, and the investigation will continue.”

The 44-year-old mom’s disappearance has been covered by news outlets across the globe after she was last seen on Wednesday, July 22, swimming near Grand Anse Beach in St. George’s, PEOPLE previously reported.

Liz was vacationing with a female friend, and surveillance footage from their rental showed her entering the water shortly before noon that Wednesday, Commissioner of Police Randy Connaught of the Royal Grenada Police Force said at a Tuesday, July 28 press conference.

Hours later, Liz was reported missing, prompting an immediate search effort involving multiple agencies.

That same evening, around 5:30 p.m. local time, her husband said she was seen “far from shore” and confirmed that she had “confidence in her swimming and location.” But there were no further sightings of Liz to add to the timeline, and by Friday, July 24, Cailen traveled to Grenada to help in the search for his wife. Unfortunately, the search by officials, family members and locals has resulted in no major breakthroughs.

But a week after Liz was last seen, Cailen wrote that he believes nothing nefarious led to her disappearance.

“After careful and thoughtful consultation with family, local authorities, the U.S. Embassy, and others here in Grenada, I join authorities in believing there was no foul play,” he wrote on Wednesday, July 29.

When Cailen announced that he was returning home to Cary, two days later, he shared his gratitude for everyone who helped assist in the ongoing search, from local police and the press to the supporters of the family’s GoFundMe page and the Grenadian people.

“Thank you so, so much,” Cailen wrote. “Every Grenadian we have encountered has warmly welcomed us and expressed so much genuine concern for Liz.”

In his update Friday, the husband also shared his deep sorrow as he is set to return home without his longtime partner.

“On a more personal note, I am simply not ready to write about all the things Liz means to me,” he wrote. “We met in 2003 at American Dance Festival in Durham and have been together ever since.”

He added, “I realized this year that Liz and I have been together longer in life than we have been apart. We balance each other, and that makes for a great partnership.”

Cailen wasn’t the only one to share his grief. Liz’s sister also posted a statement on the website on Thursday, July 30.

“Today I leave Grenada with a broken heart,” wrote Anna Watkins. “While the missing person investigation remains open, I am grieving. I am devastated, my heart hurts, and the world around me feels like a blur.”

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While she misses her sister, Watkins said that she finds solace in the fact that Liz was enjoying the warm waters and beauty of the island on the day she disappeared. She’s holding onto the memory of Liz’s “magical spirit” and “deep love for the sea.”

“I’ve reminded my kids about how the ocean is a happy place for their Aunt Liz,” wrote Watkins. “My children laughed when I added that Liz’s magic and her love for the sea could mean she became a mermaid.”

“I’ve been holding on to that idea this week,” she added. “She’s not lost. She’s exploring the sea, still sharing her magic with those around her.”