Because each platform has a unique structure and different rules for URLs, SEO URLs may be changed when migrating data from one content management platform to another.
Do I have have to use an extension from a third party or fix the URL structure manually?
On WordPress install a plugin to do 301 redirects... Yoast SEO and Redirection plugin both do this.
They allow you to input the old URLs, and map them individually to the new URL's.
I would advised first making a spreadsheet with all your old urls indexed by google, and submitted by your old xml sitemaps.
if you are not sure about your technical knowledge, I think the good choice is hiring a freelancer to check your problem. In my opinion, I do not think google ranking can migrate after changing website. Maybe this guideline can help you https://shoppingcartmigration.wordpress.com/2016/02/04/seo-urls-migration-plugin-solution-to-keep-search-ranking/
