I don't understand how Stands are connected to the Ripple Energy, which is from breathing. The third part does not seem that linked to the first two parts of JoJo.
I’m a third of the way through Part 3, and as far as I can tell, there’s minimal, if any at all, link between Stand and Hamon (Ripple) abilities. Initially, I thought the Stand was an extension of Hamon, since there’s a remark about Jotaro’s ability to fight while unable to breathe in his initial fight with Avdol, which other people on the internet have also noticed, but this doesn’t amount to much.
Discussions I found in a web search attest to this as well:
This Reddit thread and this Quora post discuss the relationship between Stand and Ripple. Posters cite Part 7, in which Hamon is indicated to be a stepping stone to Stand. (I haven’t gotten to Part 7, so I can’t judge for myself on the details.) However, this is seen as a retcon, and for the most part, people seem inclined to say that there’s not much relationship.
So, I think that due to someone using Hamon creates a Hamon current(, like electricity), and stands conduct Hamon, and I think that's how Old Joseph can send Hamon through his stand. I have also collected a paragraph from a Fandom page showing Ripple Transmission through Hermit Purple.
Joseph has shown the ability to transmit the Ripple through Hermit Purple as an extension of his body. Joseph has used this property of Hermit Purple to attack DIO or prevent him from touching him by wrapping himself in it.