In Virginia it is known as desertion as well as abandonment.  there area tow types; actual and constructive.  Constructive is when the parties still live together but say there is no sex.  Actual is actually leaving.  There has to be proven the willful desire or the intent to desert and the cutting off of the marital relationship.  In Virginia, there is no specific time period during which the desertion must continue, but you must wait a year before filing for divorce.  Whether or not the letter helps to prove abandonment would best be asked to an attorney that can review it. But i would definitely hold on to it for a while here.  Good luck.