is this sentence correct ?

I appreciate YOUR sending.... OR Thank you for sending blah blah... OR I received blah blah...

What do you mean by your second sentence??? Received 'well', and 'transparently'? No idea what you mean, but it's completely unnecessary. Obviously it was received - implied by the first sentence.

And what are you going to update them on? If you mean you will respond to the quote soon, just say that. "I expect to respond by next Friday."

Best to be clear in short and direct sentences.

I just need to confirm receipt of a quotation in a formal and polite manner. Could you give me an idea?

Thank you for your quotation.

Currently, those files are following up, we will let you know as soon as possible.

Files don't follow up; people do.

What are you trying to say?

Currently those files need following up?

It very well could be but it was such a bad sentence I didn't have a clue what he was trying to convey.

Short, direct and clear is what every sentence should be.

Maybe "Those files are being followed up", but I wouldn't say it like that.

"We are working on those files and will let you know directly."

It could, which is why I used a question mark.

I was guessing at what they meant.