If this is a toolbox that you have purchased from Mathworks, you cannot give it to someone else.
If this is a toolbox you have purchased from some other individual or software supplier, then contact them directly to ask the question.
If this is a toolbox you have downloaded from the File Exchange, then note there will be a license file that came with the software. It will contain a copyright notice, as well as conditions under which redistribution of the toolbox is permissable.
If this is a toolbox that you have written yourself, then it is simple. I would just zip the directory, then e-mail them the zip file. They could then un-zip it, and add the unzipped directory to their search path.
Simpler yet, if they are local to you, I would copy the directory to a flash drive, and give it to them. Again, they move the directory to a local drive, then add it to their search path.
If you want to make your toolbox publicly accessible, the post it on the File Exchange, or on GITHUB. Now anyone can download your toolbox.
In any of the above cases, NEVER put your own code into the official MATLAB toolbox directories, as that will cause problems.
Why do these things not work for purchased MATLAB toolboxes? Because your colleague needs to have a valid license for that toolbox. And if they do have a valid license, then they should already have the toolbox.