Authenticity cannot be settled on a video call. Bootlegs are common in this category, and the useful thing is that the information a licensed item carries is printed on it — so you can ask for a photograph of it rather than a judgement about it.
What to ask them to show
For a book: the page at the very back or front carrying the publishing and licensing details, in full and in focus.
The paper itself, with a page held up to light.
The print close up, on a dark area and on a fine line.
For a figure: the box, all faces, including the small print, plus any seals or stickers.
The figure out of the box, if it is open — and if it is sealed, ask them to say so plainly rather than implying it.
What a refusal means
These are easy photographs for a seller who has the item in front of them, and a licensed product's own packaging is not something anyone needs to hide.
"It is official, I got it from a shop" is a chain of trust rather than evidence. Ask what it says on the box.
What this page will not do
It will not tell you what print quality or paper weight to expect, or which licensing marks ought to appear. Bootlegs improve at precisely the details that get written down, and this category moves quickly.
If it matters, photograph the printed details and ask a collector who buys that line.
What protects you if you get it wrong
A bootleg sold as official is not as described: returnable for 7 days whatever the store's policy says, and reportable.
Ask about packing too — damp and spine damage are what actually ruin manga in the post, and a figure's box is part of its value.
Questions people ask
Are all unlicensed items fakes?
Not all, but anything presented as official must actually be official. A fan-made piece sold as fan-made is a different thing.
Is a sealed figure safer?
It is less inspectable. Ask about where it came from rather than trusting the seal.
Does a bootleg have any value?
Not as the official item, and selling it as one is what makes it a problem.
More: spotting a counterfeit before you bid, Metzee's position on counterfeits, reporting a seller, questions to ask before bidding on manga.