name difference in valid visa and new passport

[imhelp1]

Hi,

My mother in law has name difference issue.

1. Name in expired passport

Surname: HerFirstName HusbandName
Given names: HerSurName


2. In VALID US visa in expired passport

Surname: HerFirstName HusbandName
Given name: HerSurName


3. In new Renewed passport (this is correct representation)

Surname: HerSurName
Given names: HerFirstName HusbandName


Now can she travel to US with new passport and valid visa in old passport ?
Will she face any problem at port of entry as name in new passport and valid visa interchanged OR
there it should not be a problem as there is reference to old passport in new passport and valid visa is like old passport

Please help.

Thanks.
GR