I believe Alibre uses a proprietary version of the STEP format for it's native files.
Have you tried importing the Alibre files using the STEP option? Or just dropping the files onto the SolidWorks graphics area? Either way you will end up with a 'dumb' solid.
How many files do you need to convert? A conversion service company may be a more practical solution.
Can you post a sample Alibre part?
personally download there 30 day trial, then convert everything to step or parasolids which is best for SW.
again as Kelvin stated they will have no features just a solid blob the shape of your parts.
I am the same situation. We had Alibre for a couple of years and now have Solidworks. The past two weeks I have been trying to convert/import our last remaining Alibre files into SW. As the other replies stated, you just end up with a solid object. What I do is go ahead and open the Alibre files in edrawings (free software) then save as a 2D drawing. That way I can see all the dimensions and recreate the part in SW. It's a long and tedious process but the good side is that I tend to make design improvements as a I go along.
I do not know why Alibre had to use a proprietary format for step and other formats, but maybe that's one of the reasons why SW is still the market leader.