is this correct to say?

[Zoe2008]

Just informed by customer ......

[emsr2d2]

Only if you're writing a very brief memo or a note to a colleague and it's not important to use full sentences.

If that's not acceptable at your place of work then you need to say "I/We have just been informed by a customer that..."

If you are writing a very abbreviated note then it might say something like: "Just informed by customer - toilet flooded". "Just informed by customer - man stealing goods at back of store."