Get string after character

You need use substring function

SQL FIDDLE

SELECT substring('1245487/filename.mov' from '%/#"%#"%' for '#');

Explanation:

%/

This mean % some text and then a /

#"%#"

each # is the place holder defined in the last part for '#' and need and aditional "

So you have <placeholder> % <placeholder> and function will return what is found inside both placeholder. In this case is % or the rest of the string after /

FINAL QUERY:

 SELECT substring(source_path from '%/#"%#"%' for '#');
 FROM movies_history

If your case is that simple (exactly one / in the string) use split_part():

SELECT split_part(source_path, '/', 2) ...

If there can be multiple /, and you want the string after the last one, a simple and fast solution would be to process the string backwards with reverse(), take the first part, and reverse() again:

SELECT reverse(split_part(reverse(source_path), '/', 1)) ...

Or you could use the more versatile (and more expensive) substring() with a regular expression:

SELECT substring(source_path, '[^/]*$') ...

Explanation:

[...] .. encloses a list of characters to form a character class.
[^...] .. if the list starts with ^ it's the inversion (all characters not in the list).
* .. quantifier for 0-n times.
$ .. anchor to end of string.

db<>fiddle here
_{Old sqlfiddle}