You will always lose "what the parent was", because issues don't have a parent, but all the other fields will be kept (even if they're not on screen), as long as they have "context" for both issue types.
If for example, you set up a field called "wavelength" that only exists on "technical tasks", and another called "frequency" that is global, then fill them both in on a technical task, then move it to an issue, it will lose the value for wavelength.
You can check the field contexts from Admin -> Custom fields -> each field will list what project/issue-type it belongs to.
Also, it's not totally lost - all the old data (including parent) will show in the history of the issue.
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