There are many examples of this in action. Take the "Air Warrior Microclimate Cooling System." This is a 5.9 kg (13 pound) rig that consists of a vest full of tiny tubes that carry cooled water (with some non-toxic antifreeze added). Worn under the flak jacket it keeps the soldier cool, thus greatly reducing the "heat load" and potential for heat stroke or heat fatigue. Development on this device began in 2000 and was meant to be used by pilots in smaller (un-air-conditioned) helicopters or door gunners of larger choppers. These guys often have problems with heat (leading to heat stroke or fatigue) when operating in hot climates. The vest has also proved a life saver in armored vehicles that lack air conditioning. But here was the case of a new development (that went into service in 2003) that was invented before. A quarter century ago the army had developed a nearly identical system for tank crews. At that time the main U.S. tank, the M-60, didn't have air-conditioning. But the Israelis had added air conditioning to their tanks, recognizing that in a hot climate, during Summer, your crews were much more effective if they were not overheating. Cooled off tank crews seemed to be the wave of the future.
In 1983, the U.S. Army had its "Microclimate System" ready to go. Several generals had seen it in action and some even tried it out. These senior officers were enthusiastic about the cooling vest. But it was cut for budgetary reasons. The new (at the time) M-1 tank had air conditioning, which was preferred because it worked well with the overpressure system. This kept the air pressure higher inside the tank than outside, which prevented chemical weapons from getting in. Meanwhile, the vest found non-military use in situations where people had to be kept cool.
Another example was the M-16 rifle. At the time this was developed (by a former Marine Corps armorer in the 1950s) it was considered a brilliant application of civilian technology (the .220 Swift was a very high powered .22 caliber, or 5.56mm, hunting round) for military use. The "Stoner Rifle" (named after its inventor) was lighter and allowed troops to carry a lot more ammo. What few people realized was that twenty years earlier the .220 Swift was seriously considered as the new U.S. Army rifle, for the same reasons that got the M-16 adopted in the early 1960s. But back in the early 1930s, another new rifle was also under development, the M-1 Garand. This 7.62mm weapon was further along in development and many procurement bureaucrats were opposed to the "light weight ammo and weapon" argument. Most of these guys had never been in the infantry. The rest is history, which tends to repeat itself endlessly.
Because of the Internet this pattern is changing. The web attracts lots of data, especially on odd stuff. The web preserves that data for a long time and search engines make it easy to find out if some new and exciting development is actually something invented long ago and since forgotten.