Can I move the posts under the beam in my basement?
Possibly, but you should consult a structural engineer.  For the cost of less than a day's work for an engineer you will get an answer that you can rely on.  I know, it's unfortunate that you'd have to pay for this, but if you've invested hundreds of thousands of dollars into this house, or value your life it's probably money well spent.

The short answer, in the absence of engineering work, is no.  The reason is that those posts sit on footings that are below the slab, if you move off the center of the footings they won't actually be structurally supported, and could punch through the slab and cause the beam to collapse.