Heart and Souls is an American fantasy and comedy film from 1993 featuring Robert Downey Jr. who plays Thomas Reilly, a businessman that is attached to the souls of four deceased people, his guardian angels that died in a bus accident during his childhood, as he helps them fix problems that they have left in their unfinished lives, since he is the only one who is able to communicate with them.
The character which has the closest connection to stamps in the movie is small-time thief Milo, played by Tom Sizemore, who is also known for his other roles in Saving Private Ryan and Black Hawk Down. Milo is one of the people who was killed in the bus crash along with the three other people who die in the accident who is tasked with protecting Milo. Before he gets on the bus, we see that Milo has just failed to retrieve a book of valuable stamps that he had conned out of a young boy. The stamps are later seen to be a full sheet of 1930 Graf Zeppelins, which are incredibly rare and valuable for collectors, as explained later on in the movie.

Reproduction of the 1930 $2.60 Graf Zepplin issue sheet, Scott #C15
The Zeppelin stamp series is a set of three different postage stamps issued in 1930 that had images of the Graf Zeppelin. These stamps were issued by the United States Post Office Department in 1930 and were used only for the delivery of mail that was carried aboard that airship. They were used briefly and then withdrawn from sale due to the famous crash of the airship. The rest of the stock was then destroyed by the Post Office Department. Since the cost of stamps during the Great Depression was high, most collectors and the general public were not able to afford them. Because of this, only around two hundred and twenty seven thousand or seven percent of the total printed stamps were sold, making them relatively scarce and prized by collectors all around the world.

Mail carried aboard the Graf Zeppelin airship bearing three U.S. Graf Zeppelin airmail stamps, first issued in Washington DC, April 19, 1930, and the particular airship that was used as the model for the engraving of this 2.60 zeppelin issue, where airship number "LZ-127" can be seen on the Zeppelin image.
Later in the movie, Milo explains that he used to only steal from rich people, and taking the stamps from the kid was the lowest that he has ever been in his life. Milo then uses Thomas's body to break into a house, and steals back the stamp album, finally returning them to its owner, who is now an adult. However, after the burglary, a nervous Thomas encounters a police sergeant (who is ticketing his illegally parked car) and accidentally gets himself arrested, forcing his girlfriend Anne to bail him out of prison.
If you are interested in learning more about the zeppelin stamps and zeppelin mail, watch this stamp chat, which focuses on how you can start collecting zeppelin and airship mail too!