While I was aware that APA ignores the articles when alphabetizing the titles and organizations as authors, I have never seen an instruction to append it to the end. Endnote can correctly alphabetize the title without this “cludge”. You will need to add the word “The” to the sorting table preferences as shown in the attached image. I found this to be case sensitive (hence “the” and “The” are in my list, but you really only need “The”)
This gave me the preferred output
The European Backcross Group. (1994). Towards high resolution maps of the mouse and human genomes - a facility for ordering markers to 0.1 cM resolution. Human Molecular Genetics, 3, 621-627.
Sugimura, R., & Li, L. (2010). Noncanonical Wnt signaling in vertebrate development, stem cells, and diseases. Birth defects research. Part C, Embryo today : reviews, 90(4), 243-256. doi: 10.1002/bdrc.20195
Theriot, J. A., & Mitchison, T. J. (1993). The three faces of profilin. Cell, 75(5), 835-838.
Are you sure that the “The” should be appended in the references? If so, then you are correct, and you need to enter it as “National WWII Museum, The” in the record (double comma or “The” will be abbreviated to a T as an initial).
If you prefer your citations to include the acronym or if you need the "The National WWII Museum in the citation, the easiest fix is to hide the author and enter the Acronym,<space> or full name into the prefix field with the edit citation tool.
