Your mother-in-law certainly can enroll in Medicare Part A, but the real question is whether she is entitled to Part A coverage without paying a high monthly premium. People age
65 or older who are eligible for either Social Security OR civil service -- including federal government employment -- retirement, dependents, or survivors benefits are eligible for Medicare Part A without having to pay any premium. In other words, your mother-in-law should get free Medicare Part A coverage if either she or your father-in-law was entitled to retirement benefits (and the other one, therefore, entitled to dependents or survivors benefits) from Social Security or the federal civil service retirement system.
If neither your father-in-law nor your mother-in-law was entitled to Social Security or civil service retirement, dependents, or survivors benefits based on either one's work (one of them would need 40 quarters, or ten years, of covered work), your mother-in-law could buy Part A coverage by paying a monthly premium. For people with 30 to 39 quarters of Social Security or civil service work credits, Part A coverage costs $248 a month; for those who have fewer than 30 quarters of work credits, Part A costs $450 a month. However, there may also be a penalty added on top of these amounts for your mother-in-law if she has been eligible for Part A but did not enroll when she could have.
You should immediately contact your local Social Security office to find out what your mother-in-law's status is both under the Social Security system and the federal civil service retirement system. Once they determine her status, she can enroll in Medicare Part A at the Social Security office.