According to a 2006 study in Human Reproduction it is generally possible to conduct posthumous sperm retrieval (PHR) within 36 hours of death. Although the recommended 36 hours are "influenced by factors such as the cause of death, accompanying ventilatory support, surgical technique and the location of the procedure". The extracted sperm can then be used to conceive, typically using in vitro fertilization (IVF) and intracytoplasmic sperm injection (ICSI) techniques. This makes it all technically possible to create a child from a dead man's sperm - legal, written consent from the man (before he died) is also required in many jurisdictions.
Shai Shefi, Gil Raviv, Michael L Eisenberg, Ruth Weissenberg, Liza Jalalian, Jacob Levron, Gili Band, Paul J Turek and Igael Madgar (2006). "Posthumous sperm retrieval: analysis of time interval to harvest sperm". Human Reproduction, 21:2890-2893. European Society of Human Reproduction and Embryology.