My question was raised by this post.

Aliens crash-land at the Boston Airport (ie, in the United States). [...] The potential benefits of being able to reverse-engineer their tech alone is enough to propel the US to a new level of technology.

This happened in the early 21st century. After some years, the US have extracted enough knowledge from the spaceship and its passengers to create a huge technological gap between them and the rest of the world. Assume (if that makes any sense) that this gap is similar to the difference between WW2 and 2000's techs.

I guess that all this knowledge will leak at some point (intelligence services, private companies, bribes, retro-engineering of latest American devices...). So the question is,

How long before all other (developed) countries get to the same level of technology?

If you have to address the resulting political transformations too much, then this question may be too broad...

Skipping a bunch of me complaining about the complexities behind this, the answer is something in the frame of "they can keep their edge almost indefinitely if it gives them enough of an economic advantage". Short version if it costs too much to retool for the new technology it won't be adopted if the US is far enough ahead that other nations can't afford it. Look at the gap that developed between the US and USSR after the space race. It wasn't until relatively recently that Russia was able to catch up in the computer sciences through access to cheap components produced by outsourced offshore vendors in sympathetic countries.

This does assume an initial manufacturing monopoly, if they outsource production they'll lose almost immediately.

I think the best way to look at this is by seeing how long it took China to catch up to the USA's technology. 20 years ago, the average level of technology in China was 50-100 years outdated by Western Standards, now they have pretty comparable technologies in most areas of life; so, if you are beginning your narrative from any time period before 2000, that would be a reasonable time frame.

That said, we live in an age of hacking and surveillance where national secretes are much harder to keep than they once were. It only takes one researcher opening a bad email for someone else to gain access to an entire office building worth of research. I would not be surprised if half a dozen countries had at least some of what the USA discovered from the wreck, before they are even ready to go into production with it.

I don't think there will be any appreciable delay at all.
There are to many variables at play to answer precisely (and I assume the question will be marked as opinion based soon). But my overall line of reasoning goes like this - in this scenario the US doesn't have much head start over other nations, they do not have the infrastructure in place to produce alien technology devices at once. In short, the more secrecy there is around the alien technology, the slower the rate of adoption in the US itself, so the nation gets less benefit from it's new technology. The less secrecy, the faster it spreads.
The best use of this technological superiority, IMO, would be not trying to conceal it, but to patent it - but then you will have it produced in China and used globally the next morning (although US would profit economically the most, I guess).

UPD: the main point I see here is that initially US itself is in the petition of a developing nation - they gave reverse engineered alien blueprints and no manufacturing base to produce them. To use this technology US would need to invest into overhauling its manufacturing base first. So, using this alien technology will get expensive before it gets profitable. And in order for it to get profitable you need to actually sell it, and other countries to buy it. So in this 'peaceful' scenario the whole world gets technology, though US profits.

If the technologies are going to be used only for military, US is going to have problems with its NATO allies unless it shares. I do not think there are many pieces of technology your would want to go to war with the whole world, for example. And barring some comic-book superweapon, most military technologies take decades to integrate and implement.

The only way some alien technology can assure swift and decisive technological and military dominance is the case where it is its own manufacturing base - something like self-replicating nano-robots. And that is not 50 years worth of technological difference, it's magical philosophers stone for all intents and purposes.