How to make the following dta、

Original data has a string variable "country"

country
US
US
UK
US
Canada
UK
US
Canada

To reduce file size, I want to turn this into a numeric variable, something like

country
1
1
2
1
3
2
1
3

while also separately saving a file correspondence.dta that looks like
numeric

country
1 US
2 UK
3 Canada

Changing it to numeric to reduce the file size could be done by doing this.

encode country, gen(country2)
drop country
gen country3=country2
drop country2
rename country3 country

But since I am using country3, but not country2 (which has string label), this data now do not contain string information that I need although file size has been successfully reduced.
I need that correspondence.dta file.
How can I generate that while also simultaneously reducing file size like this?

You can save the value labels with label save country2 using country_labels.do. This will create a do-file that can be used to re-create your value label. This is sufficient if you continue working in Stata.

If you really want to store it as a second .dta you can modify the do file as follows. In the do-file editor go on Edit->Find->Replace... then type label define country2 into the find field and leave replace empty, then hit replace all. After that, do the same with , modify. Then add the following lines above the remaining part of the do file

clear
//change str50 to a bigger number if some country names are longer than 50 characters
input ID str50 country

And these lines at the end

end
save correspondence.dta, replace