Does std::move on std::string garantee that .c_str() returns same result?

I want to provide zero-copy, move based API. I want to move a string from thread A into thread B. Ideologically it seems that move shall be able to simply pass\move data from instance A into new instance B with minimal to none copy operations (mainly for addresses). So all data like data pointers will be simply copied no new instance (constructed via move). So does std::move on std::string garantee that .c_str() returns same result on instance before move and instance created via move constructor?