I received this email and I like to know  it's false or true

Sorry for the confusion, it is not visible.

i tried smc reset without any luck

"A drive that can not be seen by Disk Utility has died."

Yeah, that is what i thought. It is already at the service provider. They need 1-2 weeks to check. My only question is how much it will cost to replace the whole board

go on Apple.com.

click the flag at the bottom of the page to be certain you are on the site for your country.

find the links for "find a dealer/reseller"

contact them to see if they can replace the mainboard under the world-wide warranty.

You must make a complete backup before submitting your Mac for this repair, as the mainboard including the drive will be replaced with a new one. Make certain your repaired Mac can show its serial number after the repair, or the job is not complete.

Note: There may be an evaluation fee, to keep you from using up expensive technician time for frivolous reasons. See if you can get them to refund that cost if they do a warranty repair.

They may have to order in parts from abroad, which can take a long time. You want them to have the exact correct parts on hand before you surrender your Mac to be repaired. Be sure to obtain a firm estimate of when they expect it to be completed.

No one pays "additional customs fees" or any other bribes in the US.

Your answer is ambiguous.

Is the drive is visible inside Disk Utility, especially when you select Device-View to see each drive by Hardware-name?

If it is not, you should perform an SMC reset and see if it appears after that:

How to reset the System Management Controller (SMC) on your Mac - Apple Support

pay careful attention to which keys (on which side of the keyboard) are specified. Keys with the same names on the other side of the keyboard and not "wired in" and will not work.