Yes, because West Germany is officially called Bundesrepublik Deutschland (BRD) or Federal Republic of Germany. West Germany was just an unofficial name to distinguish between DDR and BRD. BRD merely annexed the territories of DDR and incorporated them into BRD without changing the constitution or the government, thus West Germany or more accurately BRD, which was formed in 1949, never ceased to exist to form a new state, it just expanded.