Retrieving sequence data from other file

Hello experts ,

I am new to programming and will need your help.. I have 2 very large files with the following format:

FILE1:

>MLP1019 PL4
>MLP7456 PL3
>MLP9268 PL9
>MLP6245 PL1

FILE2:

>MLP1019
STNAPLQTSNTWVSYQPSMMMSLQ
>MLP7456
PPYWYWNSAVMIFYVQPLSLLAVLLA
>MLP9268
WNANWLSPQUVSTQYWFFWFQALN
>MLP6245
TTANPLQYAVWWVSLIFIFPPALQMIF

Does anyone know how I can make an output that looks like below. I need to have the ">MLP____", "PL_", and the sequence corresponding to them.

OUTPUT:

>MLP1019 PL4
STNAPLQTSNTWVSYQPSMMMSLQ
>MLP7456 PL3
PPYWYWNSAVMIFYVQPLSLLAVLLA
>MLP9268 PL9
WNANWLSPQUVSTQYWFFWFQALN
>MLP6245 PL1
TTANPLQYAVWWVSLIFIFPPALQMIF

Thanks so much in advance!

Using awk:

 awk 'NR==FNR{A[$1]=$2;next}A[$1]{$2=A[$1]}1' FILE1 FILE2

awk 'NR==FNR {A[$1]=$2; next} ($1 in A) {$1=$1 FS A[$1]} 1' FILE1 FILE2