Copying Nintex forms will make them available on the destination site. The forms will be copied when you copy their associated list or content type. Sharegate also allows the migration of Nintex Live Forms.
Sharegate supports the full migration of classic Nintex Forms from SharePoint version 2007, 2010, 2013 or Office 365 to SharePoint version 2010, 2013 or Office 365. Sharegate does not transform SharePoint Designer and Infopath forms to Nintex Forms.
Sharegate only support migrating responsive Nintex forms from an Office 365 environment to another Office 365 environment.
To migrate a Nintex form associated to a List, you can follow the procedure detailed here.
To migrate a Nintex form associated to a Content Type, you can follow the procedure detailed here.