To tell from Wikipedia's List of related male and female reproductive organs the answer is in the affirmative.
The medical community should not consider it as inappropriate to speak of Skene's glands as „female prostate“ as in in the year 1984
Tepper, Jagirdar, Health and Geller found
„Homology between the female paraurethral (Skene's) glands and the prostate", see Archives of Pathology and Laboratory Medicine, 108(5), 423-425]2:
„(...)Homology between female paraurethral glands and the prostate has often been suggested. A means was developed that would lend histochemical support to this hypothesis. (…) The tissue was stained with antibodies to prostate-specific antigen (PSA) and prostate-specific acid phosphatase (PSAcPh) using the peroxidase-antiperoxidase method. Of those cases in which paraurethral glands were seen, 83% were positive for PSA and 67% for PSAcPh (...)“.
There is a most recent paper that should answer your question if this point of view is still accepted:
Tomalty et al., Science Direct, April 2022,
Should We Call It a Prostate?
„ (...) Whether this tissue should be called a prostate in women has been debated. (…) Gaps in knowledge relating to the functional anatomy, physiological roles, and embryological origins of this tissue have impeded the acceptance of a prostate in women. “ The scientists conducted a „literature review (...) using keywords including female prostate, Skene's/paraurethral glands, periurethral tissue, (…)", however came to the conclusions that
„(c)ontinuing to advance our understanding of the morphology, histochemistry, and physiologic capacity of this glandular tissue will clarify the characterization of this tissue as the “prostate” involved in the (female periurethral tissue) (...)“
Accordingly, and considering basic knowledge that the prostate organ is a male, not a female organ
the answer is: It is still a matter of debate within the medical community if periurethral glands (Skene's glands) are homologues of the male prostate.
As breast cancer is as typical for women as prostate cancer for men the fact that the PSA antigen which the assumption of homology was based on is a known marker of prostate tumour may lead to further search about prostate-specific antigen circulating in the blood of (female) breast cancer patients.
Prostate-specific antigen in serum of women with breast cancer that recently found „prostate-specific antigen (PSA) (...) in 30% of female breast tumours.“ From this may be infered that Skene's glands should not be considered the only tissue in women that contain cell types (at least on the level of specific stem cell potential) equivalent to prostate tissue.
For some easy reading on the issue see Health Problems News , 2018
Female prostate cancer: Do women have a prostate and is cancer possible?
"(...) Researchers have discovered that the Skene's glands share some of the same properties as the male prostate, which is located between the bladder and the penis. For example, both the prostate and the Skene glands contain prostate-specific antigen (PSA) and PSA phosphatase (PSAP), which are enzymes that can indicate the health of the prostate in males.
The discovery that these glands have similarities has led to the use of the term “female prostate.”
So, in a sense, females do have prostates, and female prostate cancer is technically possible. It is, however, extremely rare."
This article refers to
M. Goodwin in Medical news today, May 2021, Can women get prostate cancer?
(...) Doctors may find it difficult to recognize the signs and symptoms of Skene’s gland cancer because it is so rare (...). So refereing to the findings in 1984, see above, it may be infered that PSA is a natural occuring hormone of the Skine's glands.
To this, see also Parise/Rezash, Do Women Have a Prostate-Specific Antigen Level?
Conversely, thinking of solely male or female tissue one might think of Seminal vesicles which are "(...) also called vesicular glands, (...) or seminal glands)" and "(...) are a pair of two convoluted tubular glands that lie behind the urinary bladder of some male mammals.(...) They "(...) have been described as early as the second century AD by Galen, although the vesicles only received their name much later, as they were initially described using the term from which the word prostate is derived.'“. From this, the question may be infered if the female Skine's glands are (partly) homologue seminal vesicles.
Interestingly, according to Britannica Animal reproductive system "(t)he prostate, the most widely distributed mammalian accessory sex gland, is absent only in Echidna (a marsupial) and a few carnivores.", and according to Wikipedia, carnivores are animals that do not have a prostate.
Toivanen/Shen, Prostate organogenesis: tissue induction, hormonal regulation and cell type specification, Development 2017:
"Interestingly, small paraurethral glands (sometimes termed Skene's glands) that resemble a rudimentary prostate are present in female rats and humans, but not mice (Mahoney, 1940; Zaviacic and Ablin, 1998). Furthermore, these glands express PSA and prostatic acid phosphatase (PAP; also known as ACPP) (Dietrich et al., 2011; Zaviacic and Ablin, 2000), suggesting that at least some aspects of prostate development also occur in females. Although some reports suggest that Skene's glands might not be paralogous to the male prostate, as they are located caudally along the UGS, other studies have identified prostate-like epithelial buds in females that do emerge in regions analogous to prostatic buds in males (Huffman, 1948; Thomson et al., 2002; Timms et al., 1999). It is possible that low levels of androgens (...) could be sufficient for induction of prostate-like buds in females (Thomson, 2008). However, studies in rats have suggested that the presence of prostate-like buds in female embryos is more common when embryos are in proximity to other female embryos within the maternal uterus, raising the possibility that residual estrogens play a role in their induction (Timms et al., (...)"
This popular-scientific page on paraurethral cysts says that "(p)araurethral glands and ducts that are omitted in the female urethra are rudimentary analogues of the prostate gland in men" without explaining the term "omitted". From an evolutionary point of view this may insinuate that, counterintuitively, stem cells producing prostate type cells have been "deleted" in females, as other tissue that is not located in or at the urethra differentiated in prostate homology (having in mind that some mammal species do not have the prostate organ). This may speaks in favour of assuming female breast tissue partly being equivalent to prostate tissue, supported by the finding of PSA antigen in breast cancer tissue, see above. Mnemonical thesis, personal suggestion: near-urethra stem cells that would develop to "prostate" in females might be omitted, whereas in males those leading to "urethral glands" might be. Equivalents to presume: breast cells in females, seminal gland cells in males).