The first step might be to followup with the recruiter and find out as much as you can about the job - and then evaluate your ability to do (and / or to grow into) that role. You can also ask the recruiter why he/she thought you would be a good candidate for this role, to help you assess the types of skills and experience that the employer is looking for.
A new role that builds on skills that you already have (Functional Analyst) with a chance to acquire some new ones is a great way to grow your professional career. You may want to browse through the Business Analysis Book of Knowledge (BABOK) to see the techniques, tools, and competencies that are covered under a Business Analyst career path, and then see how closely your current skills (and career goals) fit into those. A 'Funtional Analyst/Business Analyst' role will probably be focused primarily on requirements elicitation (Chapter 3), requirements management (Chapter 4), and requirements analysis (Chapter 5). (Note that the BABOK covers the full range of business analysis expertise - but you don't need to know everything to start!)
These steps will give you a reasonable background and basic understanding of this opportunity - but your best source of information will be from an interview with the employer. Ask what skills and expertise the employer thinks are critical for this position. Ask about company support for training or professional development to help you build any new skills that you may need. Ask abut mentorship opportunities, and corporate supports for business analysis practices (for example, they may have reference materials, peer group supports, etc. to build BA competencies within their organization).
Plus you have everyone on Modern Analyst to give you help and advice whenever you need it! :) This sounds like a good stepping stone to grow your career and it sounds like you're ready for that - so I would encourage you to pursue it further if you're interested. Just don't go blind - collect as much information about the job and the actual employer as you can, and then decide from there.
Good luck! Sandy