You need to go to the Lead/Contact section on which you want to open the conversation, Go to Leads/Contacts section, then you will able to see all the existing leads/contacts in it.
Step 2:
To open the conversation on the Lead/Contact, search the lead in the search bar, click on the Lead which have multiple WhatsApp numbers, then go to their WhatsApp Business on productivity section.
Step 3:
Now to switch to the different conversation, click on the drop-down on that existing conversation number then you’ll find number of Contacts available on that Lead/Contact.
Accordingly, you can select which conversation you have to switch on or start. As given in below img.
Now, you'll see the chosen conversation as given in below image.