I had a job about 9 years ago working in a university office where I was essentially a full-time administrative assistant, using some software to manage various aspects of the departmental office. The software was poor, written by a student at the university actually, to fit the specific needs of the office.
Fast forward 9 years, now I am a software developer with about 5 years of development experience, and looking back, I have tons of ideas for how the software can be made better. I want to improve the existing software and, if agreeable, would be open to doing a complete rewrite down the road. I would have to work remotely since I have relocated since then. I know they are still using the same software in some degree of bad-ness, because part of it is public-facing, and from what I saw today, the styling and UI are identical to what they were 9 years ago (if that tells you anything...).
I am tempted to email the dean of the office where the software is used, but I am conflicted about how to word such an email. I want to be bold and assert that I have not only the functional but technical know-how to give them a quality product. Also, I worked pretty closely with this dean when I was there before and am convinced he'll remember me. How do I professionally offer my services without sounding like I'm saying "Hey your software sucks, and if you pay me, I'll fix it...?"
Not asking for someone to write the email for me, just want one or more basic professional guidelines to follow when doing so.