As long as it takes to complete the investigation. One hour, several weeks, months...
The time required depends on the nature of the financial abuse. And do not expect APS, the police or the DA to explain their findings about any crimes to you in any detail.
Also, the elder, an agent under a power of attorney, or a family member or friend, should explain the case to an elder abuse lawyer for a consideration of civil actions. A conservatorship may be needed, or a law suit for elder abuse may be needed. See Welfare and Institutions Code§ 15657(b) and/or § 15657.5(b) here http://www.leginfo.ca.gov/calaw.html or vist the local law library.
I suggest you develop a strong personal rapport with the APS representative. Try to assure that you are not trying to intrerject yourself into a position of financial gain. Unless the individual has made plans for incapacity where a conservator is named, you could suggest the Public Guardian, a professional fiduciary or even yourself. The facts are so different in each case that it is difficult to generalize. You are startingat the right place with the APS; now letthem do their job. If you perceive the situation is getting worse, you might ask them to consider the need of a temporary conservatorship.
I am not giving personal legal advice, but rather answering a hypothetical question from someone I don't know.