How to split a genome fasta into a fasta containing multiple short fragments?

Coding noob here.

I downloaded the RefSeq genome fasta for E. coli, and I want to create a fasta where the genome is split into multiple fragments, each with the length of 15.

For example,

"AAAAAAAAAAAAAAAGGGGGGGGGGGGGGG......"

becomes

"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAG"
"AAAAAAAAAAAAAGG"
etc.

I'm trying to do this in R as I don't have any python skills. Currently, I have,

# Read in E coli genome fasta file
eco_genome <- readDNAStringSet("data/GCF_904425475.1_MG1655_genomic.fna") 
eco_genome_string <- eco_genome %>%
  as.character() %>%
  paste(collapse = "")

I think I need to use a substring() function??

Once I have the new fasta containing the 15 nt fragments, I want to map them to a different genome fasta. (Basically, I want to know which 15 nt sequences are shared between the two genomes.)