In the description from the shop i can find that it is possible to login with the joomla login. When i use now the JFB login i am not logged in the shop. Is this possible?
I'm confused as to what you're asking here. Can you help clarify a bit more as to what is, or isn't working?
When a user logs in using JFBConnect, they are logged into a Joomla account. There is no difference between a JFBConnect/social network user and a standard Joomla user.. they are the same thing. I'm not sure of any reasons that logging into JFBConnect wouldn't log the user into a 3rd party extension *unless* that 3rd party extension is simply bridging to another shopping cart solution outside of Joomla. I don't think that's how Aceshop works, but I'm honestly not sure.
I hope that helps explain,
Alex