Usually. Most states will admit a foreign will to probate even if it doesn't meet all the requirements of a will as long as it is valid in the state in which it was executed. (The term foreign will is how courts describe another state's will. It doesn't mean a will from another country.)
For instance, some states require that a will be attested to by two witnesses. Other states may require three witnesses. If you execute your will with two witnesses and it is valid in your old state, the new state will admit the will to probate even though it doesn't meet the requirements of a will in the new state which may require three witnesses.
However, wills are not always recognized by the new state. As an example, Texas and many other states recognize holographic wills. A holographic will is one that is wholly in the testator's handwriting. It doesn't require witnesses if it is wholly in the testator's handwriting. Florida does not recognize holographic wills and will not recognize a foreign will if it is a holographic will even though it is valid in the prior state where it was written. Florida Probate Code, §732.502. Just to be safe, if you move to another state you should talk to an attorney who handles estate planning to make sure your will is valid in your new state.
Copyright by Robert Ray a Texas inheritance attorney.
Tell me what happened
Write to me through the contact form: what happened, roughly when, and who is involved. I read these myself. Writing means our first conversation can be about your situation instead of getting me up to speed.
This page is general information about Texas law. It is not legal advice about your situation, and reading it does not create an attorney–client relationship. These matters turn heavily on specific facts and specific dates, and the law has exceptions this page does not cover. You should not take, or refrain from taking, any action based on this page. Discuss your circumstances with an attorney who can advise you on them.