Not sure if I fully understand your needs but what about this?
Two surveys:
In survey 1:
Code:
Condition equation question: {if(rand(0, 1) == 1, "A", "B")}
Say they got option B - they now see this end message
Here is your link to take part in the second survey which will become active on (Date):
Code:
https://yourplatform.com/123456?Condition={Condition}
You could also pass the user generated ID here, so you have a link between survey 1 & survey 2 per respondent
In survey 2, hidden short free question at the start: Condition. This gets prefilled with the condition shown in survey 1. You can now show or hide questions based on this. So if respondent link is Condition B -> show questions related to Condition A for second survey.
The difficult part is that respondents will have to save your link somewhere which isn't ideal.