So she penned a letter to a man in Lawrenceville, New Jersey - one she and her family had spoken to over the past 10 years but had never met.
"She said, 'Is there any chance you'd consider walking me down the aisle?' " Thomas told the Post. "I said, 'Oh, there's a big chance.' "
Thomas said the early notice gave him time to prepare himself so he wouldn't be "blubbering" as he walked her through the church.
"The last 10 years, I watched my children graduate from high school and college and I'm probably going to be able to see them get married," he said. "And that same 10 years, Michael's family went without him.
"I had a life to live because of him, and his family did not. It was important for me to do this very small thing for her."
Stepien said her father, Michael Stepien, was on his way home from work one night in 2006 when he was shot and killed by a teenager during an attempted robbery in Swissvale, a borough outside Pittsburgh.
Thomas, 72, told CBS affiliate KDKA he was "on death's door" when he received Michael's heart. He said his own had been failing for years and, by 2006, he was suffering from congestive heart failure.
The last day in September, he said, Stepien's family gave him a gift.
"I remember telling them how grateful I was for this new lease on life and that I realized the sacrifice they made was extraordinary," Thomas said of his first letter to the Stepiens.
I had a life to live because of him, and his family did not. It was important for me to do this very small thing for her
Since then, Thomas, who is married with four grown children, said the two families have exchanged many handwritten letters and phone calls. Every holiday, he sends Michael's wife fresh flowers.
On Sunday, Jeni Stepien said, when the door to St Anselm church in Swissvale swung open, she felt "my dad was right there with us".
"This wasn't just about me," she told the Post from the airport, moments before the couple headed out for their honeymoon. "It was also about making my mum and my sister and Tom see everything had come full circle."
And when it came time for the first dance, Thomas once again took her hand.
"He did my father-daughter dance with me and then handed me to my mum," she said, adding that he "made this dream come true."
She wrote on Facebook: "It truly was the best day of MY ENTIRE LIFE!"
"To be able to bring my dad home and have him at my wedding was an absolute dream COME TRUE!" she wrote. "Not to mention that being married to the best person that was hand picked just for me was beyond words the best thing that has ever happened to me."
In 2014, more than 29,500 people received organ transplants in the United States and an average of 22 people a day died waiting for them, according to data from the Department of Health and Human Services.
More than 120 million people are registered as organ donors.
Stepien wrote on Facebook that she hopes her family's story will inspire others. "If I helped just one person change their mind to become an organ donor, my wish in sharing my story has come true," she said.
Thomas said he hopes that the gift he received from Stepien and her family will impact others as much as it has impacted him.
"This young woman had such wonderful motivations - to say to the world, 'Organ donation is really important. We want you to be aware of it.' "
