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If you have a choice to stick up to the current version and carry on with the things then it is fine but if this is not a choice then move towards redirecting 301 to all the pages to new URL structure is something you should be doing. Obviously this affect your traffic and SERP rankings for certain keywords but along with the migration if you also working on the quick marketing campaign (as you are taking over some other website) which may includes Press Release, Blog posts about it, mailer to all your subscribers and social media.... this will help people coming and visiting your website from multiple places and this will help you retain your SERP rankings and traffic quicker than normal.

Yes I did, thank you for the information. I had a feeling that could be it but I wanted to make sure that I wasn't missing anything.