It's easy to understand why anyone would be reluctant to get tested for Alzheimer's. It has replaced cancer as the most dreaded disease for most people. The truth is that
Alzheimer's disease still cannot be verified until autopsy. There are dozens of dementias, of which Alzheimer's is the most prevalent. Until we have reliable testing, it's a process of elimination. The official diagnosis is "dementia of the Alzheimer's type."
I have to assume that your concerns are typical: your father-in-law is forgetful; he misplaces things, and maybe exhibits some personality changes. I'm also assuming that you and your sister-in-law have already broached the subject with him unsuccessfully numerous times and he gets very angry when you do.
I suggest that you leave the subject alone for now until you feel you've regained his trust. If he wants to talk to you about what's happening, avoid using the "A" word; instead use terms like "memory-loss," MCI (mild cognitive impairment) or even "dementia."
In the meantime, share your concerns with his primary physician and set up a check-up for him. Your father-in-law needs a thorough physical to eliminate other possible causes of his decline. Several reversible conditions mimic dementia, among them dehydration, drug reactions, low-grade infections, NPH ("normal pressure hydrocephalus" or water on the brain) "“ even ingrown toenails or toothaches. Although most doctors include memory testing as part of a major check-up, you might want to reiterate the need for this with his doctor. Let the doctor take the reins. If he asks what's going to happen at the check-up, feign ignorance and just remind him that you are all there for him.