The following example should work provided your fileb does not happen to contain the customer code string elsewhere in the record.
awk '
BEGIN {
while (getline < "filea" > 0){newcust[substr($1,2)] = substr($2,2)}
close ("filea")
}
{
for (oldcode in newcust)
{
if (match($0,oldcode == 1))
gsub(oldcode,newcust[oldcode],$0)
}
print $0
}' fileb
If fileb separates the customer code and the address by whitespace, replace...
if (match($0,oldcode == 1))
gsub(oldcode,newcust[oldcode],$0)
with...
if ($1==oldcode)
$1=newcust[oldcode]
HTH