When was used (written) in print in a letter the word "Hello" for the first time and by whom?

Not too sure about this but I believe the word 'Hullo' was first used by The Artful Dodger in Charles Dickens 'Oliver Twist'.
As for 'Hello', I think you are refering to a letter written by Thomas Edison in 1877
"Friend David, I do not think we shall need a call bell as Hello! can be heard 10 to 20 feet away.
What you think? Edison - P.S. first cost of sender & receiver to manufacture is only $7.00."

Source

Viv

That's what I was looking for Viv. Thanx! and...goodbye.

Below from Wikipedia

Many stories date the first use of hello (with that spelling) to around the time of the invention of the telephone in 1876. It was however used in print in Roughing It by Mark Twain in 1872 (written between 1870 and 1871),[1] so its first use must have predated the telephone:

"A miner came out and said: 'Hello!'"

Earlier uses can be found back to 1849.[2] It was listed in dictionaries by 1883.[3]

The word was extensively used in literature by the 1860s.[4] Two early uses of hello can be found as far back as 1826.[5]

* Report on the trade in foreign corn, and on the agriculture of the north of Europe. by William Jacob, 1826. page 213

"On this occasion she switched it on to a patient who was awake and who merely said 'Hello Sister, what's the matter with you...'"

* The Every-day Book: Or Everlasting Calendar of Popular Amusements, Sports, Pastime, Ceremonies,...By William Hone, 1826 Page 1370

"Then hello boys! hello boys! shout and huzz....

here are many different theories to the origins of the word. It may be a contraction of archaic English "whole be thou".[6] Another source may be the phrase "Hail, Thou", as in the Bible; Luke 1:28 and Matthew 27:14.

The Germanic languages share an ancient morpheme that may be the origin of hello: English, hail; German, heil; Scandinavian, hell/heil; old Norse, heill. The core meaning may be something like "safe, healthy" and related to the English word "whole" (also to "holy", "whole" and "health"), i.e. physically sound. See also "hale and hearty".

Telephone

The word hello is also credited to Thomas Edison specifically as a way to greet someone when answering the telephone; according to one source due to expressing his surprise with a misheard Hullo.[7] Alexander Graham Bell initially used Ahoy (as used on ships) as a telephone greeting.[8] However, in 1877, Edison wrote to T.B.A. David, the president of the Central District and Printing Telegraph Company of Pittsburg:

"Friend David, I do not think we shall need a call bell as Hello! can be heard 10 to 20 feet away.
What you think? Edison - P.S. first cost of sender & receiver to manufacture is only $7.00."

By 1889 central telephone exchange operators were known as 'hello-girls' due to the association between the greeting and the telephone.[3]

In Hungarian, Hallod? (pron. roughly as British hullo) means "Do you hear [it/what I am saying]?" and the answer is Hallom (pron. like hullom) for "I hear [it/what you are saying].". Another story suggests this as a source for the use of hello on the telephone: the Hungarian inventor Tivadar Puskas was in America when Alexander Graham Bell invented the telephone. Soon Puskas began work on a telephone exchange. According to Thomas Edison, "Tivadar Puskas was the first person to suggest the idea of a telephone exchange". Puskas' idea finally became a reality in 1877 in Boston. It was then that the word hallom, which later became hallo/hello was used for the first time in a telephone conversation when, on hearing the voice of the person at the other end of the line, an exultant Puskas shouted out in Hungarian "hallom" "I hear you".

Hullo

Hello may also be derived from Hullo. Hullo was in use before hello[citation needed] and was used as a greeting and also an expression of surprise. Charles Dickens uses it in Chapter 8 of Oliver Twist in 1838 when Oliver meets the Artful Dodger:

"Upon this, the boy crossed over; and walking close up to Oliver, said 'Hullo, my covey! What's the row?'"

It was in use in both senses by the time Tom Brown's Schooldays was published in 1857 (although the book was set in the 1830s so it may have been in use by then):

* "'Hullo though,' says East, pulling up, and taking another look at Tom; 'this'll never do...'"
* "Hullo, Brown! where do you come from?"

Though much less common than it used to be, the word hullo is still in use, mainly in British English.

Hallo

Hello is alternatively thought to come from the word hallo (1840) via hollo (also holla, holloa, halloo, halloa).[9] The definition of hollo is to shout or an exclamation originally shouted in a hunt when the quarry was spotted:[9]

"If I fly, Marcius,/Halloo me like a hare." - Coriolanus (I.viii.7), William Shakespeare

Webster's dictionary from 1913 traces the etymology of holloa to the Old English halow and suggests: "Perhaps from ah + lo; compare Anglo Saxon ealā".

According to the American Heritage Dictionary, hallo is a modification of the obsolete holla (stop!), perhaps from Old French hola (ho, ho! + la, there, from Latin illac, that way).[10]

Where do you think you Americans got your word 'holler' from?

All these forms of hello/hallo/hollo/holloa/holla/hullo (some of them existing as verbs as well as exclamations) are said by the Oxford English Dictionary to probably be from the verb 'hallow', an old word meaning 'to shout in encouragement, especially of dogs in the chase; shout to attract attention'. That is itself derived from Old French 'halloer' , which 'is of imitative origin'. By imitative the editors must mean of dogs in full cry: certainly a dog or hound in the company of others makes a distinctive noise when it sights prey, quite different from a bark or howl, which is a signal to tell other hounds of the sighting and to give chase.

The British say 'Hullo!' and 'Hallo!' as well as 'Hello!'

Foxhunters, when they were still allowed in Britain , traditionally yelled (hollered?) 'View, halloo !' on spotting that the pack had seen a fox and to signal to the other huntsmen to take up the chase.

The OED dates the form 'hello' from the late C19 .

For 'holler' it says 'Chiefly dialect and North American colloquial'. It dates from the late C17 in England. The definition the OED gives is ' cry out, shout, especially in protest or complaint'. It derives from 'hollo/hollow' the Late Middle English verb and noun which is a variant of 'hallow' (above)