Gmail conversation view is a Gmail setting that allows you to set whether emails of the same subject are grouped together. And cloudHQ label sharing allows sharing all emails in conversations or just emails explicitly added to the label. This is controlled with option Do not share entire conversation – just individual email.
If you disable the option Do not share entire conversation – just individual email then once you share an email by applying a shared label on it, all emails in that conversation (such as replies and forwards) are automatically shared.
So if you want cloudHQ to keep sharing all emails in Gmail conversation (such as replies and forwards) automatically, then disable this option.
On the other hand, if you do not want to automatically share all emails in Gmail conversation (such as replies and forwards), then enable this option.
In the cloudHQ web interface the option is called Conversation View:
BTW, you can learn more how Gmail decide to group emails into conversations in this support note.