Do You Need to Dissolve an LLC if You Move to a Different State?
You do not need to dissolve your LLC and create a new one in the state to which you move it. There is no obligation that a company be established or formed in a state in which it does business. This means that an LLC does not need to be formed in the state in which it is based, nor does a corporation have to be incorporated in that state. In fact, a great number of corporations are actually incorporated in Delaware regardless of where they physically are located or do business. (However, for 99% of all corporate purposes or corporations, there is no particular advantage to Delaware incorporation.)
Registering Your LLC in Your New State
It is also not required that you transfer it in any fashion. What you would need to do is to register with your new state as doing business there; any businesses in a state, regardless of the state of formation, should be registered with the state in which they are operating. This is a fairly straightforward process, though the exact mechanics and details will vary by state. You can contact the state's department of revenue or department of state—which are usually the agencies responsible for this process and, if not, they at least will be able to direct you to the correct department or agency.
Consulting with a Tax Advisor or Business Attorney
However, before doing that, you may wish to speak with a tax consultant or advisor. Each state has its own rules on how it taxes businesses, both domestic (created within that state) and foreign (established in other states). They also have their own rules about filing fees and paperwork requirements. It is possible that it may be advantageous to you to dissolve the existing limited liability company while reforming it in the new jurisdiction. It could potentially result in either saving your business money or reducing your paperwork burden or both.
So in summary: you do not have to establish an LLC in the state in which the business is located; you would have to register to do business in that state; and it is possible that it would be worthwhile to end the existing business and form a new one in your new state. If you go that route, a local business attorney can make the process painless and easy.