The link is added automatically and the pay link is switched on if it was not already. The customer taps it and sees the invoice, with a Pay button if you have connected Stripe.
Why there is no PDF attached
A picture message carries a PDF badly, costs several times more, and lands as a file most people will not open on a phone. The page behind the link says everything the PDF would.
Why it might refuse
Texting your customers needs the carrier registration approved first — see Register your business so it can send texts. Until then the button explains why rather than reporting a send that would never arrive.
Where the conversation goes
The text lands in Virtual assistant, in the thread with that customer. When they reply "can I pay Friday", it arrives in the same place, with the invoice that started it directly above.