So I checked some quote poster designs and billboard designs on Pinterest but one thing was confusing.
Some were using a full stop in the end of quote (i.e., just before the "). For example:
"This is a bla bla bla quote by someone."
-- Author Name
And some were avoiding it:
"This is a bla bla bla quote by someone"
-- Author Name
So as you can see in 1st example, there's a full stop after someone. But it's not yet part for a poster or billboard yet. It's just a text form in the details of this question.
But in case of a poster or billboard design, it would be the primary text and so I'll use it in bigger font size.
And I'm not sure whether to use that full stop or not. Personally, the dot and quotes combination ( ." ) looks a bit noisy/clutter to me (it could be only me), so I tend to remove it. But I'm not sure if it's right thing to do or not.
If we talk about English grammar, I think you should use the full stop. Somewhat similar is discussed here.
But I'm not sure when we make it part of a design. So should you use the full stop or can it be avoided?