Form a DE corportion and then merge the LLC into the DE entity so that all assets and liabilities of the NJ LLC are transferred to the new DE corporation as the successor in interest under merger law. The NJ LLC convertible note would become liability of DE Corp and convertible note agreement can have a provision dealing with the change of rights to receive LLC units to now be read as DE corporation shares.
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Delaware has a conversion statute, which allows entities to convert into a Delaware corporation without having to go through a more complicated merger process. You will also need to follow New Jersey law as it relates to reorganizations. The filing fees for Delaware are $164 (or more, I believe depending on how much stock you authorize); there may be fees associated with the process in New Jersey. If you are doing business in Massachusetts, you will also need to re-register the company as a foreign corporation.
Just filing the papers alone can take anywhere from a few days to a few weeks, depending on whether you order expedited processing (at additional cost) from Delaware; it will also take additional time to draft the appropriate corporate documents, such as the bylaws, stock purchase agreements and certificates, and most likely in your case, a shareholders' agreement.
Liabilities transfer with an entity in a Delaware conversion; however, you would need to ensure that your angel's purchase agreement and note are drafted carefully to maintain conversion rights and value given the change of equity form -- it might be simpler to effect the reorganization before taking on the investor.
Also note that the IRS and state revenue agencies may treat this reorganization as a taxable event, so it is highly recommended you consult with a tax advisor so as to understand any tax liability. Finally, if you don't already have one, you should also retain a business attorney who can assist you in ensuring that the whole conversion and investment process is completely correctly and smoothly.
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You should consult with a business law attorney in your area to make sure you are in full compliance in working thru this transaction. There are numerous moving parts and it needs to be done correctly. Do not try and do this on your own.
As mentioned before, Delaware allows conversions and you will also want to follow NJ law. You may want to consult both an attorney in your area as well as an NJ attorney. Most business attorneys, like myself, know DE law pretty well as their statutes invite many companies across the country to form in their state. However, it is always a good idea to involve an attorney of your previous jurisdiction (NJ) as well as Boston to ensure that you are in full compliance. If done correctly, this process can be done fairly quickly (maybe less than a month).
While obviously the golden rule applies here, (those with the gold make the rules) it is worth asking the question as to why a Delaware C corporation since there are significant tax disadvantages to shareholders to being a C corporation before the time is right (think double taxation).
There are two key facts which are omitted from your writeup which could allow for a more indepth and better answer. The first is what is your business and business plan - what is your plan for growth and how much outside capital, if any, will you need going forward (my guess is that since you started out as a NJ LLC you did not have delusions of grandeur)- the second fact is what will the convertible note convert to - common or preferred - if preferred why not preferred units and keep the tax structure better for the current members? It seems to me that converting to a DE LLC as part of the proposed financing might be a happy middle ground for all involved.