Ryan,
Sorry for the delayed response.
There's no way to move that popup. The JFBCInvite module is using the 'old' style of invitations from Facebook, and that popup is frankly broken. There are ways to change the CSS to make the popup 'overflow' into the sidebar. If you send me the link to the page you have JFBCInvite module on, we can likely help.
With that said... JFBConnect 4.1 (to be released at the end of this week) will use the new Requests system of Facebook. It uses a text link or image that a user can click and a 'real' popup will come up for the user to select their friends. Additionally, you can send invitations to your users from the admin area. Even better, tracking of who's sent request and who's acted on them is included. There will also be a {JFBCRequest ..} tag you can use to easily add it to your site.
So, all around, it's a much better solution. If you can wait a few days, I'd recommend you do. We're very excited for the new system.. and very excited to not have to deal with overflow issues too much anymore from the JFBCInvite module
One caveat with all the above is that Facebook's new request system uses the Facebook Canvas, and that requires that you have an SSL certificate. Setting up the canvas is easy.. the SSL is under $20/year.. so shouldn't be overly burdensome, but can still be inconvenient. Just making sure you know.
Hope that helps,
Alex