I have seen some people using 'grateful' in the beginning of a statement like.
Grateful, if you can send me the details of the conference,
Can someone tell me if this usage is correct or not?
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I would rather say no. This would sound better to me:
I would be grateful if you could ...
With the comma, it's incorrect.
Without the comma, it reads sort of okay to me, but it's very very informal. (note: can should really be could.)
Grateful if you could send me the details of the conference.
This is short for the more correct sentence,
I would be grateful if you could send me the details of the conference.
It's a stretch, but this might be admissible as part of a larger request. For example:
I'd be satisfied if you filled out those forms for me. Grateful, even, if you submitted them yourself.
This is not grammatically ideal, so it'd only really work in an informal context. I doubt it applies to the instances you've seen, but I thought it would be worth mentioning for posterity.