Any suggestions would be greatly appreciated.
The items don't actually show up in your workbench, but if you try to build something then you should be able to do so as long as the connected settlement has the necessary resources.
Have you set up connecting Supply Line (Build mode, target a settler, should be an option to make a supply line)
Yeah, otherwise they'll stop their current chore, which isn't a serious issue, but could leave you short of food for example.
I'd advise using unnamed generic settlers as they do travel -slowly- between the connected settlements. I do remember a recent post on here from someone who had assigned one of the companions to a supply line and ended up struggling to find them for a quest.