Can I wait 6 weeks to fix a broken crown?

Unfortunately, you cannot have that part recemented on the back. The material could have been faulty, or, more likely, the bite was too high, causing the crown to fracture.  The tooth may need to be reprepped in order for there to be enough space for proper thickness.  If the crown material is too thin, it can also shatter.  
Usually the dentist who did the first crown is the one to replace it.  Another dentist may charge you for a whole new crown.  Good luck!

In a situation like this you want something to protect the tooth from further breaking or moving. A new crown is needed if you can see a dentist were you are now ask them to make a temporary crown for the tooth. And when you get back to your regular dentist make a new crown and maybe discuss why this one broke off. It could be the material or the design of the crown or the bite.