Joint (MFJ) versus separate (MFS) is not a matter of whether they are living together or apart. It is a matter of how a married couple chooses to be treated under the tax law.
Generally speaking, a couple that is married at the end of the calendar year can file either MFJ or MFS. Also generally speaking, MFJ is more likely to result in a lower tax bill than MFS.
As kaneohe says, whoever is doing their taxes should check the official IRS rules to be absolutely certain, but in all likelihood they can and should file MFJ.
"At times the world can seem an unfriendly and sinister place, but believe us when we say there is much more good in it than bad. All you have to do is look hard enough, and what might seem to be a series of unfortunate events, may in fact be the first steps of a journey." Violet Baudelaire.