In Georgia a "conservator" is responsible for the finances and a "guardian" is responsible for the person. If the conservatorship in Oregon includes both (some states have a single designation that is responsible for both), you would want to have the Oregon court move the conservatorship/guardianship to you and then transfer the conservatorship/guardianship to Georgia.
If the Oregon conservatorship is only financial, you can still transfer, but if you want a guardianship as well that would be a separate matter.
It generally isn't too difficult to transfer the case to Georgia after you have been named guardian/conservator in Oregon.
Feel free to call my office and I can answer more specific questions if you'd like.