The Girl with the Make-Believe Husband : Book 2 by Julia Quinn

While you were sleeping...
 
When Cecilia Harcourt finds out her dearest, and only, brother has been injured on the battlefield in New York, she bravely travels across the Atlantic, determined to nurse him back to health. But after a week of searching, she finds not her brother but his best friend, handsome officer Edward Rokesby. He's unconscious and in desperate need of her care, so Cecilia vows that she will save this soldier's life, even if staying by his side means telling one little lie...
 
I told everyone I was your wife.
 
When Edward come to, he's more than a little confused. The blow to his head knocked out six months of his memory, but surely he would recall getting married. He knows who Cecilia Harcourt is - even if he does not recall her face - and with everyone calling her his wife, he decides it must be the case. 
 
If only it were true...
 
With this deception, Cecilia risks her entire future - but when the truth comes out, Edward may have a few surprises of his own for the new Mrs Roskesby...