output:
But if I assign the output of cat fileA command to variable a and then echo the content of variable a, the newline characters are replaced by blanks, which I don't want, because I want to use the variable to insert the table into another file and for that it must keep the original newline characters.
The output is this:
How can I fix this?

The backtick operator has that "feature", if you can call it a
feature. You didn't describe what you really want to do other than
the above sentence so we are left to guess, but here is one way to get
at a particular line in a file and store it into a variable:

By the way, you had $A instead of $a in your script, and that won't
work (you will get empty output from the echo because $A was not set
but $a was set.)

There is also the $() operator which works under Linux's sh and bash
shells, but does not work on all UNIX's Bourne shells. But since this
is a Linux forum, and I suspect you are on Linux, you could write the
above as:

The $(...) syntax has the advantage in that it can be nested, while
the backtick expression, `...`, can't for obvious reasons.

bg

Yes, that was a typing mistake, I meant echo $a, instead of echo $A. I am correcting it right now.

a=`cat fileA | grep three` will only assign the third row of the table (since that is the only row where "three" pattern appears) to variable a instead of assigning the whole table ot it, wich is what I want.

I am tring to store several tables into variables so I can then replace a pattern inside a template file.

template.txt:
suppose fileA fileB and fileC are tables
I want to store those three tables into a variable so I can then replace patternx patterns with the content of the table with the following comands:
" template.txt | "s/pattern2/"$b"/g" | "s/pattern3/"$c"/g" > output.txt
Right now I have solved this problem without needing to store the files into variables, but It would be good to know how can this be done so I can make my script faster.

In bash putting $a in double quotes preserves the newlines
echo "$a"
1 one
2 two
3 three

But the newlines in "$a" will cause sed to fail:
A way around this is to replace the newlines in "$a" with the string '\n' which GNU sed will output as a newline.
The sed 'r' command reads the contents of a file and appends it after the contents of the pattern space.
This is similar to but not the same as what you are trying to do.

Thanks, you tought me something new. I was also thinking in replacing the newlines in the original tables with my own delimiters using sed, then use sed to replace the patterns for the contents of the tables and finally replace my own delimiters with the newline characters.