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I just wanted to write a letter to head of an English tests center and wanted to make sure what I have is correct, what I am writing is this:

Hi Mary, happy new year and hope all is well

I am Blah and then the rest of the email I am gonna write...
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In a formal email, to someone who is not a friend or relative, it is best not to ask one of these questions:

•Hi, how are you? •How are you doing?

...because it could be considered too casual and friendly. It is better to express interest in the person’s well-being by starting with one of the following statements:

•I hope all/everthing is well. •I hope all/everthing is well with you. •I hope this message finds you well.

Hi Mary, happy new year and hope all is well.

Hi Mary, happy new year and I hope this message/note finds you well.

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3

I would prefer something like this:

Hi Mary, happy new year and I hope all is well

Without the "I," it's not clear who's doing the hoping.

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1

Yes it's fine.

It's very much elided, with "hope all is well", but then "happy new year" is very much elided from "I wish you a happy new year".

This degree of elision is normal and common with seasonal greetings and other such salutations.

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