Whether or not the field groups appear in ACF for edit would not have anything to do with custom post types.
You need to figure out where/how the CPTs were created in the old theme and all of the settings used to create them. You can then re-create them using ACF, or with another plugins with the same settings.
ACF 5.6.7 did not include custom post types and taxonomies, this was not available until 6.1. So they had to be created somewhere else. ACF will not automatically import or recreate these.
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