FamilySearch has New York probate records for county courts but "most records end in the 1920s." I'm particularly interested in Montgomery county where FamilySearch only has records through 1922. Where can I find probate records for the succeeding years?
Probate records for New York State are kept by the Surrogate's Court in each county. The website of the New York State Unified Court System says:
Genealogy Research Since 1787, probate records like wills are filed and kept by the Surrogate's Court in each county. These records are available from the courthouse and appointments may be needed to view the records. There may be a fee to access some of the records. Use the Court Locator box to find the Surrogate's Court in the county you're interested in.
Addresses for Montgomery County can be found via the county court locator for the Surrogate's Courts Outside New York City. Unlike some other county courts in New York State, there does not appear to be an online genealogy guide for the Montgomery County Surrogate's Court.
The Probate Record Pathfinder at the New York State Archives gives an overview of the process plus some information about the (limited) records held at the archives. They say:
The Surrogate’s Courts do not accept email requests for research assistance. The preferred method of inquiry is in writing via U.S. Mail. Frame such requests in succinct and specific terms, stating name of decedent and date of death. Applicable search, copying, and authentication fees may be charged. Researchers should keep in mind that in all time periods, many people died without wills, and there may have been no court-supervised distribution of their estates.
More recent records relating to the estates of persons who died without a will (intestate) are found in the Surrogate's Court. In such cases, the court appoints an administrator, whose duties are similar to those of an executor, and distribution of the property to heirs is made according to state law. In instances when an executor declines to assume responsibility, a “renunciation” is made, and the court appoints an administrator.
New York State also provides an online copy of the Freedom of Information Law which describes the rules governing public access to records, and the fees authorized for making copies of the records.
The FamilySearch Wiki article on Montgomery County gives links to the collections you've already checked (which stop in 1922) and notes:
Additional Probate Indexes and Abstracts
Additional probate indexes or abstracts can sometimes be found using search phrases such as Montgomery County, New York Genealogy probate wills in online catalogs like WorldCat or the FamilySearch Catalog.
Also, one caution: not all probate files on FamilySearch are in a database with the word "probate" in the title. See Using a card index to find Probate records for an example from New York City, where probate records appear in a mixed batch of court records.
For the most up-to-date information, it may be worthwhile to consult Chapter 6 in the New York Genealogical & Biographical Society's new publication, New York Family History Research Guide and Gazetteer.