Transferring quest items

I want to get the Tapestry Shred from Gwen, but I unknowingly grouped with somebody who already got it with my current char. Can I start a different character and get the shred from her, then transfer it to my main char via storage or mail? Thanks.

Good fortune

Yes you can obtain the shred on a different character, and then transfer it via storage to your main character.

Not quite sure what you mean by referring to mail

There is no mail in GW. Storage is the only way to transfer items between characters on the same account (outside of "here, hold my crap while i load onto a different character" but that's inefficient)