If you have a Swedish personal number and you are planning to move from Sweden, you should, in accordance with the Swedish laws, notify Skatteverket about your moving abroad. After your notification, you will be deregistered from the Swedish Population Register.
If you move abroad from Sweden and plan to stay away for a year or longer, you shall no longer be registered in Sweden. In such cases, you should notify the Swedish Tax Agency that you are moving abroad, no later than a week prior to your departure.
The notification form can be downloaded from the link below or you can get it at the Service Office of Skatteverket (Servicekontoret), which is located in front of the Health School. After filling the form with required information, the form can be handed in to the Service Office, or you can just drop it in the Post Box of Skatteverket.
Download notification here.