To prevent users from linking to one version of a URL and others linking to a different version (this could split the reputation of that content between the URLs), focus on using and referring to one URL in the structure and internal linking of your pages. If you do find that people are accessing the same content through multiple URLs, setting up a 301 redirect32 from non-preferred URLs to the dominant URL is a good solution for this. You may also use canonical URL or use the rel="canonical"33 link element if you cannot redirect.
QUOTE: “Starting April 21 (2015), we will be expanding our use of mobile-friendliness as a ranking signal. This change will affect mobile searches in all languages worldwide and will have a significant impact in our search results. Consequently, users will find it easier to get relevant, high-quality search results that are optimized for their devices”. GOOGLE

Ask for a technical and search audit for your site to learn what they think needs to be done, why, and what the expected outcome should be. You'll probably have to pay for this. You will probably have to give them read-only access to your site on Search Console. (At this stage, don't grant them write access.) Your prospective SEO should be able to give you realistic estimates of improvement, and an estimate of the work involved. If they guarantee you that their changes will give you first place in search results, find someone else.