Yes. Actually, the information flow is the other way around. The amino acid sequence is similar *because* the DNA is similar.
There’s a direct translation table (called the codon sun) between DNA and amino acid sequences. While there are different possibilities for DNA sequences to still code for the same protein (like there are multiple binary files, just in different formats, that will produce the same image), if a whole sequence is similar it’s very likely that it evolutionary came from the same ancestors, therefore sharing similar DNA.
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