I love this quote. I see the meme everywhere, with various styles of punctuation. I've seen it obviously incorrect several times, but now my eyes are blurring and I haven't seen it the way I would format it anywhere. Here it is without any punctuation: I would write it like so: Here's to strong women: may we know them, may we be them, may we raise them. How would you punctuate it, and what punctuation is the most technically accurate? I feel like you could correctly use periods, commas, or semicolons in the latter portion of the sentence, but the colon shouldn't be skipped over, correct? I have yet to see it written like that. Instead, it's written with period or another comma at the beginning. The more I dissect it, the more I think this is one of those "no one loses, but no one wins" scenarios, and I don't like ties. So I've come to you, who are wiser than I. Or is it, "wiser than me?" Shit.
The one you wrote seems fine, but I also think a period after 'women' works. It's asyndeton when the 'ands' and stuff are left out. I don't think any meaning is lost or added between the period and colon.
I think implicit in the toast (Here's to strong women) there's a call to action, so for me the colon and list of items separated by commas works best. If you decompress / expand what the meme is saying, it becomes something like this, right? With regards to strong women, I exhort you to: spend time with and get to know take the effort to become take the effort to raise your daughters to become one of these magnificent beasts.
As correct punctuation, it would be a colon at the end of Women, and semi colons in between the list of additional thoughts with a period at the end. You would only use commas if you were listing things and using an "and" before the last one. Here's to strong women: may we know them; may we be them; may we raise them. However, it can be just as the OP wrote it, which is a poetic style, where you don't use punctuation, but use line endings to impart a pause. Either way is correct.
Here's to strong women, May. We know them, May. We be them, May. We raise them. That's the line spoken to the single mother and grandmother called May of a single mother who has a daughter during a brief speech over a glass of sherry.
Here's two strong women. May we know them June we be them July we raise them. Some kind of paradoxical accelerated time shift device applied to a Thelma and Louise story, where the characters regress from knowing themselves (ie learning of their dead selves), to being themselves, to raising themselves, all in the space of a 3 month time period.