I solved this issue by using in the latex document
\usepackage[T1] \usepackage
The first statement enables T1
font encoding and the second enables the use of modern latex fonts.
I even had been using (only) the first statement the whole time (which did not fix this issue by itself) but adding the second statement did fix it and the Word document saved from Acrobat Pro (X in my case) was displayed correctly.
See the answers at this https://tex.stackexchange.com/questions/115080/cannot-copy-text-from-the-simplest-pdf-file?rq=1 question for more details.