Is it permissible for her to exhume her husband's grave and transfer his remains for burial in another city, in fulfillment of his verbal will, after 10 years have passed since his death?

It is not permissible to exhume a grave except for an extreme necessity or an overriding interest, such as burying a Muslim among the graves of disbelievers. The described situation is not a reason to exhume the grave; because that disrespects the deceased and may lead to the breaking of his bones or the decomposition of his body. The location of the grave is not important, and one should supplicate for the deceased and give charity on his behalf.