Porting stemming algorithm from Java to Python
Specific suggestions:


Python will throw an IndexError if you try to access an element past the end of a list, so you don't need to check index &gt;= len(s) or offset &gt; len(s).
After the simplification above I would inline the __check methods as assertions.
Throwing an exception and catching it again within the same context is a code smell - it's too much like goto. Why not just return instead? Or let the user know the input could not be processed?
You don't actually use any OOP in your code, so apply might as well not be within a class
In the same way I think you could just use a List[str] for dest.
Checking the type of an argument is unpythonic. Basically you're responsible for passing some value which can be used by the code. And with type checking (below) you could even enforce this at a test or linting stage.
Abbreviations make code harder to read. I would expand things like destination, position and command.
Magic values like R and D should be named constants to improve readability.


General suggestions:


black can automatically format your code to be more idiomatic.
isort can group and sort your imports automatically.
flake8 with a strict complexity limit will give you more hints to write idiomatic Python:

[flake8]
max-complexity = 4
ignore = W503,E203


That limit is not absolute by any means, but it's worth thinking hard whether you can keep it low whenever validation fails. For example, I'm working with a team on an application since a year now, and our complexity limit is up to 7 in only one place. Conversely, on an ugly old piece of code I wrote without static analysis support I recently found the complexity reaches 87!)
I would then recommend adding type hints everywhere and validating them using a strict mypy configuration:

[mypy]
check_untyped_defs = true
disallow_untyped_defs = true
ignore_missing_imports = true
no_implicit_optional = true
warn_redundant_casts = true
warn_return_any = true
warn_unused_ignores = true


As a Java developer I'm sure you'd appreciate the clarity this lends to the code.