I think you should 1st ask yourself what is your business level of maturity? Can grow it into a good business under these circumstances?
Here are some pointers regarding the options you've given:
1. Closing the company is an option that should be considered in my opinion if and only if
(a) The information/assets/capital lost as a result of losing your partner can't be recovered within a reasonable amount of time.
(b) There are legal / financial obligations that you shared with your partner and once he leaves, risks to you personally increase dramatically e.g. you'll need to invest in 500K$ to replace your partner's investment/lost capital.
2. Your 2nd option is composed of two requirements (a) finding a new partner, (b) relocating the company. Therefore I think each component should be addressed separately, (a) locating a new partner is typically the best option for most cases as it allows you to continue focus on what you do best, share responsibilities and optimize work thus increasing your success chances. (b) Relocating the company is not always the optimal move in some cases you had some resources and connections that are location dependent e.g. banks, permits, workers, etc. Obviously if your business is location agnostic then as I've stated before in my humble opinion this is the best move for most cases.
1. Last but not least is the tendency of founders to try to handle loss of other founders/participants by
taking these missing members roles and responsibilities to themselves. These type of a solution has a few flaws: they take more time, require more money and tend to increase chances to make mistakes due to having less experience. Our goals should always be focused on what we do best, get people (new partners, board advisors, technical advisors, etc) to help us handle what we don't know, so our time to market is quickest with lowest cost. Unless you can bridge the gaps left by your partner a few weeks while pushing forward on the product development side, I would strongly advise against such a move.
Hope this helps.