awk
to the rescue!
assumes the second file has unique keys unlike first file (if not you need to specify what happens then)
$ awk 'BEGIN {FS=OFS=";"}
NR==FNR {a[$1]=$2; next}
$1 in a {print $0,a[$1]}' file2 file1
A;1;30
B;2;20
A;3;30
ps. note the order of files...