Split fasta file based on groups in header information and output as separate files

I have a fasta file containing the sequence of a gene across different species. In total there are around 900 samples and 12 species. (Each sequences is over multiple lines and longer than 100bp.)

My fasta file looks like:

>Species-1-samplenameA
CTATCCTTAAACGCATATCTCGCACAGTAACTCCCCAATATGTGAGCATCTGATGTTGCCCGGGCCGAGTTAGTCTTGTGCTCACGGAACTTATTGTATG
>Species-2-samplenameB
AGTAGTGATTTGAAAGAGTTGTCAGTTAGCTCGTTCAGGTAATGGTTCCTCACACTACGTCAAAATAAGAGAGCGGTCGTGACATTATCCGTGATTTTCT
>Species-3-samplenameC
CACTACTATCAGTACTCACGACTCGATTCTGCCGCAGCCACGTATCGCCAGAAAGCCAGTCAGCATTAAGGAGTGCTCTGGGCAGGACAACTCGCATAGT
>Species-3-samplenameD
GAGAGTTACATGTTCGTTGGGCTCTTCCGACACGAACCTCAGTTGGCCTACATCCTACCTGAGGTCTGTGCCCCGGTGGTGAGAAGTGCGCATTTCGTTC

I want to split this file in one fasta file per species.
I think it’s possible to use the awk function for this but I’m stuck. Does anyone have a script/code that might help me?

Thanks a lot.

from Bio import SeqIO

for record in SeqIO.parse("myfile.fa", "fasta"):
    species = record.id.split('_')[0]
    with open(f"{species}.fa", "a") as f:
        SeqIO.write(record, f, "fasta")