
Is that really an invention or an achievement?

Thank you for the interesting question! It is both an invention and an achievement. The definition of "invention" says that it refers to an item produced or a new process. The "use of fire" is definitely a process.
In Merriam Webster's definition, #3 is most relevant.
Full Definition of invent
transitive verb
1
archaic : find, discover
2
: to devise by thinking : fabricate
3
: to produce (as something useful) for the first time through the use of the imagination or of ingenious thinking and experiment
Wikipedia has an article on "Cultural Invenion" :Cultural Invention is any innovation developed by people that is not of a physical construct.[1] Cultural inventions include sets of behaviour adopted by groups of people. They are perpetuated by being passed on to others within the group or outside it. They are also passed on to future groups and generations.[2
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