Paul Pogba, Manchester United and Barcelona were among the masses around the world to breathe a sigh of relief as the Wild Boars team finally emerged after more than two weeks trapped underground.
"This victory goes to the heroes of the day, well done boys, you are so strong," the Manchester United midfielder tweeted after Tuesday's 1-0 win.
"Amazing news that all of the Thai kids are out of the cave safely! I'd like to send out shirts to them! Is there anyone who can help with an address?" he tweeted.
The last of the group was finally extracted on Tuesday, 18 days later, after a painstaking and dangerous international rescue mission led by Thai Navy SEALs.
FIFA said it had been informed "that due to medical reasons, the boys will not be in a position to travel to Moscow".
"FIFA's priority remains the health of everyone involved in the operation and we will look into finding a new opportunity to invite the boys to a FIFA event to share with them a moment of communion and celebration," a spokesman said.
But both the team and their rescuers could be in line for a trip to Old Trafford after Manchester United invited them to their home ground this season.
"Our thoughts and prayers are with those affected. We would love to welcome the team from Wild Boars Football Club and their rescuers to Old Trafford this coming season."
United extended a similar invitation to the 33 Chilean miners who were trapped underground for 69 days in 2010, giving each of them a shirt with his name on the back and a number reflecting the order they were rescued.
The boys will also head to Barcelona's Camp Nou stadium after the Spanish giants invited them to next year's Barca Academy International Tournament and a home game.
Rescuers had weighed up several options to save the boys, including keeping them in the cave through the months-long monsoon season.
But they were prodded into the dangerous task of "diving out" the team through submerged chambers and claustrophobic passages as oxygen levels in the cave plummeted and rains menaced.
The group were led out in three batches by a team of 13 international divers flanked by the Thai Navy SEALs, who greeted each successful rescue with a "Hooyah" on their Facebook page.
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