As there are many options involved in this scenario, it is highly recommended to contact a Funeral Director in the destination state to plan the final transportation of your loved one.
Transportation can either be by car or by airline, and there are services that do just that, so they are familiar with all the differing state regulations for documentation and transportation requirements.
It is possible for a friend or family member to do the final transportation, but they need to be fully informed regarding the requirements and documentation.
Though embalming is never required for the first 24 hours, there are some states that do require it when crossing state lines. If the family is planning on a traditional service in the destination state, they may choose to have the body embalmed prior to a long final journey to better preserve remains.
Transporting cremated remains (cremains) is, of course, much less expensive, however it may not be an option for many families, for religious or personal reasons.
Interstate transportation, whether by ground or by air, can be expensive and all costs should be presented per the Federal Funeral Rule. Make sure you know what you are being charged for and that there are no hidden charges.