Generally speaking, if you as an applicant with qualifications from an EEA land other than Sweden have a licence, authorization or corresponding certification from your home country, then you will usually be granted the corresponding authorization in Sweden upon application to the Swedish National Electrical Safety Board (in accordance with directive 2005/36/EC). You must enclose supporting documentation with the application verifying that the you have a licence/authorization in your home country. There is a fee of SEK 2000 for granted authorizations. There is no fee for applying.
Hope this helps. Obviously things differ from country to country but a competent spark should have no problem after having a walk through a few site to see how they do things.I do however have a suspicion that if you would like to certify installations you would have to do their exam.