The person who was the journal's point of contact during the reviewing process (hereafter referred to as the "review owner") should add the review to Publons, this will make it easier to have the review verified. Once this is done the review owner can add collaborators via the review's "Progress" page (accessed via the "Progress" column in your review history).
The review owner can copy the collaborate URL and send it to the reviewers they worked with. Those reviewers will then be able to follow the link to "claim" the review and end up with a copy of it in their review history. The review owner maintains control over the review's display preferences, content, and the status of any review collaborators.
Please note that while some journals acknowledge the possibility of collaborating on reviews without explicit consent, many would consider this a violation of their terms and conditions. As such, we suggest that you request permission from a journal before sharing a manuscript with any potential collaborators.