Can I use the modal verb "Should" to express that I own something?

Suppose it’s about to rain. One should bring his umbrella to go out. Is it grammatically correct to say –

It looks like it will rain. He should have his own umbrella with him, just in case it does.

It looks like it will rain. I should have my umbrella with me, just in case it does.

Or one should own a book. Is it ok to say –

You should have the book.

Or one should eat something like (breakfast/ Dinner/ burger) then can I say –

You should have it/ lunch.

As far I know Should have + past participle can mean something that would have been a good idea, but that you didn’t do it.

I am little confused about this grammar rules.