If you move before the decision has been made to issue your card has been taken from one province to another your card would be invalid. For example if you move from Vienna to another province before a decision has been reached about your application, you may have to reapply in your new province. One possible course of action might be to change your MeldebestätigungMeldezettel Austria requires everyone living in Austria (both Austrians and foreigners) to register their place(s) of residence with the local authorities. The confirmation of this registration is called a Meldebestätigung (EN: confirmation of registration), although it is still affectionately known to many by its former name (the Meldezettel). This is done at your Meldeamt in the Gemeinde or Bezirk you live in. You are required to do your registration within three days of arrival. It is important to do this also because your qualification for permanent residence starts to run from the point of your registration. and to send it to the respective authorities of your new place of residence and the old place of residence. That way the office for your new residence may be able to receive the documents through from your old province (or request further information).
If you apply for a card and receive it and subsequently move to another province, your renewal process may be delayed as the authority in your new place of residence will probably need to get your previous file from another province. It is therefore worth ensuring that if you hold a five-year card that you do not leave renewal to the very last minute prior to your card expirying.
H/T Friedrich Bruckner