According to the Shared cM Project, a 1390 cM match is in your case much more likely (90%) to be either a half sister or an aunt/niece than it is (10%) of being a first cousin, half-aunt or half-niece. Ancestry recently started providing this type of percentage information if you click on the little "i" icon that is to the right of the shared cM and segments. I don't have a relative with 1390 cM to check, but I would expect their percentages should be close to what the Shared cM Project gives.
There are two articles you should read.
- Escape from the Overlap Zone, by Leah Larkin.
Leah talks about differences in cM and shared segments between half-siblings and aunts/uncles/nieces/nephews based on Andrew Millard simulations. She says they can sometimes be distinguished from one another if they are on one's paternal side, but not on the maternal side.
- Half sibling or Nibling? A first look at the 25% relationship data, by Kitty Cooper.
Kitty provides nice graphs of real data collected comparing segments vs cM for half-siblings and niblings and talks about the difference between maternal and paternal. She also introduces largest shared segments, and notes the difference between half paternal siblings, half maternal siblings and niblings for that. Unfortunately, Ancestry doesn't give you longest segment information.
Those two articles really tell you the best you can do with just total cM and number of segments.
In other words, total cM and number of segments may not be enough information to differentiate the relationship, but that's all AncestryDNA provides for you.
AncestryDNA does show shared matches. You can use a clustering technique (like the Leeds method) and see if you can separate the people into your husband's four grandparents. Your husbands' close match, either as a half-sibling or aunt/niece or first cousin should fall into the two clusters representing his father's side. Then you can look at the two clusters and see if those people's trees in each cluster provide you with information to identify some of your husband's family on his father's side.
If your husband is really interested in finding who his father is, then he should download his raw data from AncestryDNA and transfer it to Family Tree DNA, MyHeritage DNA and GEDmatch. He may want to test at 23andMe as well who don't take transfers. Unlike AncestryDNA, all the other companies provide the actual segment matches and provides you with tools to display and work with the segments themselves. There is a chance that your husband's match has additionally tested or transferred data to one of the other sites. If so, the greater detail the segment data provides likely will allow you to determine what her relationship is to your husband.
Even if your husband's match has not tested at any of the other sites, you still might find another close match at one of the other sites who did not test at AncestryDNA, and that could help you discover who your husband's father is.