Hello. I am always confused about this. I think American and British people use it in different ways.

Someone is writing a letter and starts saying "I am very happy to write you". I was going to correct write TO you. But is the original wrong?

Thank you!

Some years ago, my British teacher marked as wrong my closing sentence in a letter (FCE level) to a friend. I had witten "Please write me soon." Emotion: smile
I was then taught that British and American English differ on this (... write you => AmE; ... write to you => BrE).

Here are three extracts from three dictionaries.

* 1 *

to send a letter or similar message to someone, giving them information or expressing your thoughts or feelings:
She hasn't US written me/UK written to me recently.
SOURCE: Cambridge online dictionaries

* 2 *
to put information, a message of good wishes, etc. in a letter and send it to sb:
She wrote to him in France. (...)

I wrote a letter to the Publicity Department. (...)
(NAmE) Write me while you’re away.
(NAmE) He wrote me that he would be arriving Monday.

SOURCE: Oxford dictionary

* 3 *
to write a letter to someone

write to
I've written to my MP, and to the city council.

write somebody American English
Chris hasn't written me for a long time.

I wrote her several letters, but she didn't reply.

SOURCE: Longman dictionary
The original one is correct.
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 Tanit's reply was promoted to an answer.
I should've added that "to" is dropped in BrE when write is followed by two objects, as in: "He wrote me a letter" (also, "He wrote a letter to me").
Thank you ALL very much!!! You helped me a lot!!!

Not I see it much clearer.

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