Is it possible to have multiple surveys where one survey would be completed a month but it would not be possible to move onto the second month without first completing the first month for a particular user?
if not would it be possible to have similar functionality with question groups?

That is not possible with the core LimeSurvey package. You may be able to do it with a remote script, cron job or plugin but that would require considerable development.

Maybe with a question validation at 1st group

date("M") > 3 : always false before march, then user can get to 2ng group before march ?

Yes, that may work in a single survey with updating responses allowed.

I was thinking more of multiple surveys. A cron job that fires a PHP script to:

- Check the data from the first survey
- Finds all responses from 1 month ago
- Uses the API to load new tokens in the second survey and send invitations for those respondents

tpartner wrote: Yes, that may work in a single survey with updating responses allowed.

Not updating : just answer persistance because respondant can not submit it.
I think it can be great to have Question validation on www.limesurvey.org/manual/Question_type_-_Text_display question. Then we can add everything wanted in such question,
And for example have the warning tip shown only before march.

tpartner wrote: I was thinking more of multiple surveys.

If using multiple surveys : gitlab.com/SondagesPro/SurveyAccess/surveyChaining i need to do the README and doc : but it's near done for this (except the delay …)