The Nobel Prizes have not been awarded posthumously since 1974 (with one exception, Ralph Steinman, who died two days before being awarded the Nobel Prize without the knowledge of the Nobel committee). In the specific case of the Nobel Prize for Physics, the Nobel Prize is awarded when a theory is either proven or has stood the test of time, not when it is postulated - a recent example is the awarding of the Nobel Prize to Peter Higgs and Francois Englert after the discovery of the Higgs Boson in 2013 by scientists at CERN, even though their theory dated from the 1960s.
Einstein's solution to the Photoelectric effect was proven experimentally by Robert Millikan in 1914, and Einstein duly received the Nobel Prize for Physics in 1921. Millikan also received the Nobel Prize for Physics in 1923, partly for his proof of the Photoelectric effect and also for his famous oil-drop experiment where he determined the charge of a single electron. This award isn't without controversy as he discarded some of his data from his oil-drop experiments which would have given a greater degree of error than he stated when he produced his results, this and other controversial Nobel Awards have led to the tightening of the rules over time.
In the case of Relativity, there were many experiments and observations carried out during Einstein's lifetime that supported the theory however it wasn't until 1971 that Hafale and Keating proved that time-dilation occurs in objects in motion, with additional proof made in 2015 by LIGO with the detection of gravitational waves from the merger of two spinning black holes. Sadly for Einstein, both experiments were carried out after his death in 1955.
Links: [Hafale and Keating proof] (http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/airtim.html)