We all know that Elvis' very first private record in 1953 consisted of My Happiness and That's When Your Heartaches Begin.
That's When Your Heartaches was written by Fred Fisher, George Brown and William Raskin.
Fred Fisher

Real Name: Albert von Breitenbach
German-American songwriter (born September 30, 1875 in Cologne, Germany - died January 14, 1942 in New York City, New York).
Inducted into the Songwriters Hall of Fame in 1970. For the remarkable 'Peg O' My Heart' and some more, Alfred Bryan wrote the lyrics.
George Brown

Real Name: William Joseph Hill
Pseudonym of Billy Hill, allegedly used because he didn't want his name reversed to 'Hill Billy'.
William Raskin
American lyricist, born November 3, 1896 in New York City, New York; died April 8, 1942 in New York City, New York.
The original version of That's When Your Heartaches Begin (1937) was recorded by Shep Fields and his Rippling Rhythm Orchestra with the vocals of Bob Goday:

Shep Fields (Sep. 12, 1910 - Feb. 26, 1981)
In 1936, he signed with Bluebird Records as the Fields' Band and with his group's distinctive sound known as "Rippling Rhythm", his recordings soon became a hit on the Billboard charts. His band was featured in the film "The Big Broadcast of 1938" and he conducted his orchestra at the Academy Awards ceremony in Los Angeles in 1939. In 1941, his group billed as "Shep Fields and His New Music", continued to record for Bluebird and made a USO tour to Europe towards the end of World War II.
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The Ink Spots recorded the song on December 23, 1940 in New York. The spoken interlude was by Orville (Hoppy) Jones and the single was re-issued in May 1952, when it became a hit for this group.

The Ink Spots
The Ink Spots were a popular African-American vocal group who gained international fame in the 1930s and 1940s. Best known for their recordings of Pop ballads, The Ink Spots were frequent chart toppers totaling over 50 hits in their 17 year recording career. Their best selling record "If I Didn't Care" sold over 19 million copies and is currently the 7th best selling single of all time. Bill Kenny (leader) disbanded The Ink Spots in 1954 however many spin-off or imposter groups have been performing and recording ever since. In 1948 the group was awarded with a plaque from the Negro Actors Guild for the efforts in "breaking down the walls of racial prejudice".
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It's common knowledge that this version by The Ink Spots was the version which inspired Elvis to record that one day on July 18, 1953:
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Elvis sang it again on December 4, 1956 - while jamming with Jerry Lee Lewis and Carl Perkins:
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Elvis liked the song, that is clear. He recorded it officially some six weeks later at Radio Recorders Studio 1 - Hollywood, California on January 13, 1957:
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And he rehearsed it for his 1968 TV Special on June 24, 1968, as can be heard here:
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Other versions of the song
Billy Bunn & His Buddies - 1952
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David Whitfield - 1958
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The Beatles - 1960 rehearsal at Paul's house
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LONE STAR - (Spanish version) - 1968
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Mina, from her album "Baby Gate" - 1974
(Clip: Starchy & Husky episode 87 - May 8, 1979)
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SOURCES
http://davidneale.eu/elvis/originals/list8.html#S1488
https://www.discogs.com/Elvis-Presley-All-Shook-Up-Thats-When-Your-Heartaches-Begin/release/6020216
http://www.findagrave.com/cgi-bin/fg.cgi?page=pv&GRid=6844852&PIpi=15772679
https://www.discogs.com/artist/322272-The-Ink-Spots?anv=Ink+Spots
https://books.google.nl/books?id=ezXaAAAAMAAJ&pg=PA366&lpg=PA366&dq=that's+when+your+heartaches+begin+1942&source=bl&ots=PmFHgpANt-&sig=lOONgasoZEOpCXktHDNfsonfw0k&hl=nl&sa=X&ved=0ahUKEwiClO_43dfOAhUHJMAKHeCnDKcQ6AEILjAB#v=onepage&q=that's%20when%20your%20heartaches%20begin%201942&f=false
http://www.keithflynn.com/recording-sessions/570113.html
https://www.muziekweb.nl/Muziekweb/Cat/SingleSearch/Search?q=that%27s+when+your+heartaches+begin&catalogue=
.