Yes, many times, it's certainly not uncommon to find people migrating from Asana to Jira (all its flavours, not just JWM).
Most of the ones I've done have been along the lines of
- Housekeep what we've got in Asana, cleaning and changing the shape of items to be more aligned with the Jira issue setup we want to be using
- Export the items we want to keep (usually this means "only open stuff")
- Import them into Jira with CSV or a REST based script that reads our exports and pokes it into Jira in a different shape
But you don't have to do it that way, some people integrate, so that the Asana-favouring people can carry on using their tool, and the Jira-favouring people use their preference. There's a pile of integration tools at https://marketplace.atlassian.com/search?query=asana (some of which can also be used to migrate - set up a sync, let it drag across what you need, then dump Asana)
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