Try:
awk 'BEGIN { FS=OFS="\t" } NR==FNR { seq=$1; sub(/^[^\t]*\t*/,""); if(NR==1)hdr=$0; hold[seq]=$0; next } FNR==1 { print $0, hdr; next } ($1 in hold) { print $0, hold[$1]; next } { print }' fileB fileA Try:
awk 'BEGIN { FS=OFS="\t" } NR==FNR { seq=$1; sub(/^[^\t]*\t*/,""); if(NR==1)hdr=$0; hold[seq]=$0; next } FNR==1 { print $0, hdr; next } ($1 in hold) { print $0, hold[$1]; next } { print }' fileB fileA