Does executor of a will by law in N.J. have to supply a named person with a copy of the will.

Yes - part of the executor's duty is to supply beneficiaries with a copy of the will.  Once the will is probated, it becomes a public document.  there is no time limit in which you must probate the will.  Unlike some other states, it is not an offense to fail to probate a will.  There is a restriction or waiting period however, and you must wait 10 days from the date of death, and probate on the 11th day.