An associate wrote an open letter (email) of condolence to a friend who'd lost a child. The letter stated that that deceased was now an angel in heaven with wings. What is the ultimate source of this belief?
In Heaven: A History (1995: Yale University Press) the authors, Drs. Colleen McDannell and Bernhard Lang, state that Emanuel Swedenborg (1688-1772) had a pivotal role in bringing about a changed view of heaven, including the idea that angels are humans who have died and gone on to heaven, rather than a separate race of pre-created beings as mainstream Christianity had held for many centuries previously. See especially Chapter 7: "Swedenborg and the Emergence of a Modern Heaven."
Swedenborg based his teaching that all angels were once people primarily on his own claimed experience of meeting and talking with them in the spiritual world. For example, he says in Heaven and Hell #311:
Swedenborg also states, however, that this is the teaching of the Bible if the Bible is properly understood. For a brief summary, written from a Swedenborgian perspective, of the Biblical arguments in favor of angels and devils as human beings who have died and gone on to the spiritual world, see the article What the Bible Says: Where Angels Come From.
Here are the basic points made in the article, accompanied by supporting citations from the Bible:
For my own overview of and introduction to Swedenborg's teachings about angels (I am a Swedenborgian minister and scholar), including a section on where angels come from, see Who Are the Angels and How Do They Live?
Swedenborg's Heaven and Hell has been translated into many languages, and has had a large circulation throughout the world since it was first published in Latin, London, 1758. Outside of various statements in the Bible itself, it is the primary source of the common modern belief that people become angels after death.
However, Swedenborg did not say that angels have wings. Rather, he said that they are fully human in appearance.
Within Christianity, the belief that humans become angels seems to stem from a misinterpretation of Jesus' words:
It seems many people incorrectly interpret "like" and "equal to" to mean "identical to."
Mainstream Christianity has never taught this; the early church fathers argued over many things concerning angels (whether they are only spirit or have material bodies, what categories of angels exist, etc.), but it doesn't look like they had to argue against the idea that men became angels. Not one of the thirteen commentaries I've read make the claim (or even leave open the possibility).
Outside mainstream Christianity, a few groups do teach that humans become angels:
According to the Latter Day Saints:
And LDS teaching on angels:
The Swedish philosopher/scientist-turned revelator Emanuel Swedenborg, in his book Heaven and Hell published in 1758, wrote that angels are man's perfect form (they are the same race; angels are pure/purified humans).