A journalist sent to the island of Samos to cover the migrant crisis for daily Aftonbladet found the letter in a waterproof bag on a beach where boatloads of migrants have been arriving daily from Turkey.
The newspaper said it wanted the public's help to return the emotional letter to its rightful owner.
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"Maybe they are together, or maybe life has forced them apart ... We are asking you who are reading this to share it on one of your social media channels on the internet," it said.
"If you have written it, we hope you will excuse that we quote a few lines:
My Rose,
I promise you, I will love you until the last minute of my life.
I promise you, I will not let anything separate us, whatever happens ... "
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The letter was found on October 29 and was being kept at Aftonbladet's office in Stockholm. Written in Iraqi Arabic, the letter is signed by Hamody, a nickname often used for Mohammad or Ahmad.
More than 800,000 people desperately fleeing war and misery have landed on Europe's shores since the beginning of the year, according to the UN refugee agency.
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