Using Automator to move subtitles files Is it possible to use Automator to automatically move a subtitle file .srt to the folder where a video file with the same name is located?

Let's say I have a file ~/Videos/MyVideoFolder/my_video.avi and I download a file ~/Downloads/my_video.srt, I want it to automagically move it to  ~/Videos/MyVideoFolder/.

The subtitles files are identifiable by its extension .srt, but videos can be of any type.
Consider using AppleScript instead of, or in combination with, Automator. Automator does not easily fit into workflows that require conditional branches.

Conditional branches are steps within the workflow that perform an action depending on some state or situation. In this case, if the video file is present in the destination folder.

AppleScript can handle this type of task; as could a perl script or other scripting language.

See Can Automator branch based on the value of a variable or the result of a step? for a script based approach combined with Automator. 

Scripted Approach

For tasks like this I prefer scripting languages like perl. Below is a script that should get you started - or that others can build on. It is untested, so treat with care:

#!/usr/bin/env perl

use strict;
use warnings;

use File::Basename; # for fileparse

# WARNING: lack of error checking

# Use: ./move_srt.pl &lt;path to source folder&gt; &lt;path to destination folder&gt;

my $source_path = shift;
my $destination_path = shift;

# Get the video file names - without their 3 or 4 letter suffixes
my @destination_video_files = glob($source_path.'/*');
my %named_video_files = map { $_ =&gt; fileparse($_,qr/\..{3,4}/); } @destination_video_files;

# Get a list of srt files
my @source_srt_files = glob($source_path.'/*\.srt');

foreach my $source_srt_file (@source_srt_files) {
    print "[Encountered] $source_srt_file\n";

    # Strip suffix and check if video exists with same name
    my $named_srt_file = fileparse($source_srt_file,qr/\.srt/);
    if (exists($named_video_files{$named_srt_file})) {

        # Move the matching srt File
        system('/bin/mv '.$source_srt_file.' '.$destination_path);

        print "[Matched] $source_srt_file\n";
    } else {
        print "[Unmatched] $source_srt_file\n";
    }
}