Workaround:

Click on the right top corner on the settings gear inside the browser page. Deactivate sponsored links. (I added a couple of files to results also, but I don't see it doing any good for the problem)

Close.

Problem is solved.

I would say Amazon link is doing something nasty with search words.

I don't see how that is a workaround for this. It still removes the first word when anything copied is pasted into the search bar yet is still fine when pasted into the address bar. No behaviour has been changed.

It also doesn't matter what search engine I set as the default, it still looses the first word.

Also worth mentioning that starting in safe mode with add-ons disabled gives the same behaviour.

Also my laptop does the same as my desktop.

Did you turn off the feature to flip your input up to the address bar, or does that make any difference? This is the preference for that:

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button accepting the risk.

WARNING: Changing preferences through this interface not officially supported Hidden settings edited using the about:config tool are explicitly not supported, which means that Mozilla makes no guarantees they will be supported in the future, or that Mozilla will fix them if they break. Mozilla does not test these preferences, and will not in the future. That includes security and performance testing which these preferences may affect.

[Warning added by moderator.]

(2) In the search box in the page, type or paste handoff and pause while the list is filtered

(3) Double-click the browser.newtabpage.activity-stream.improvesearch.handoffToAwesomebar preference to switch the value from true (move query to address bar) to false (keep query in in-page search bar)

Thank-you. That has solved the issue.