Your punctuation is fine. You have a parenthetical (non-restrictive) clause that should be set off with commas. It can also be at the beginning or end of the sentence.
All of these are fine:
According to the local team, the part was delivered yesterday.
The part was delivered yesterday, according to the local team.
The "Please be informed" phrase is just throat-clearing, an introduction that is not material to the sentence content.
One more way to consider writing it:
Please be advised that the part was delivered yesterday (according to the local team).