This prints the first field and then every subsequent field until end of the line.
$ awk '{for (i=2;i<=NF;i++) print $1,$i}' file
P04637 1A1U
P04637 1AIE
P04637 1C26
P04637 1DT7
P04637 1GZH
P04637 1H26
P04637 1HS5
P04637 1JSP
P04637 1KZY
P04637 1MA3
P04637 1OLG
P04637 1OLH
P04637 1PES
P04637 1PET
P04637 1SAE
P04637 1SAF
P04637 1SAK
P04637 1SAL
P04637 1TSR
P04637 1TUP
P04637 1UOL
P04637 1XQH
P04637 1YC5
P04637 1YCQ
To get exactly what OP request, no more, no less:
awk '{print $1,$2 RS $1,$4 RS $1,$3 RS $1,$5 RS $1,$23 RS $1,$11 RS $1,$14 RS $1,$16}' file
P04637 1A1U
P04637 1C26
P04637 1AIE
P04637 1DT7
P04637 1XQH
P04637 1MA3
P04637 1PES
P04637 1SAE