Summary: I'm an IT contractor, and have some self-made source code (my IP) to solve certain problems a lot of clients have. I want to legally "give" that IP to my clients, without explicitly charging for it (the fee for it is included in my day rate, and so already paid). If I do this, is it legally binding and/or does it open me, or them up for other problems?
In my off-time, I've spent some time re-creating some of the clever solutions I've seen elsewhere. Typically this is done by reading a tonne of web pages, putting scraps of information together and iterating a bit to make a solution. None of the original is used to do this, other than my memory of what it was. These solutions are expressed as computer source code.
I tend to try to make these "generic" such that they could be customised to fit any future client, so they're similar but different to the originals. I don't foresee any claim from previous clients over these works (or at least, that's not the subject of this question).
Now working at a new client, I can "cut and paste" my solution into their environment. This saves me time, and so saves them money. I use this capability as part of my negotiation of day rates and such like.
I'd like to formerly give rights to the "cut and pasted" source code that I've used at my new client. I of course want to retain ownership of my copy, but make it very clear that I've given them some of my IP and that they can do anything they like with it going forward. The purpose of this is partly legal, but mostly to make it super explicit that it's taken place - a bit of "PR" if you like. I'd want to hand them a legal document explaining what's happened, and a description of what it is they've received, why it's good for them, etc.
My lawyer has "Assignment of Intellectual Property" templates (https://www.lawbite.co.uk/legal-and-business-documents/139/assignment_of_intellectual_property), which look to me like they'd work nicely. I can of course have the lawyers check over my edits of those templates before I send them. However, in that template there's a "schedule" of the items being assigned which is supposed to list the price I'm charging.
My question is, can I either make the price £0, or else somehow express that the fee has already been paid as part of the day rate? Does doing so somehow have side-effects to me in the future?
If I were to charge £0, would a (pedantic?) client require me to send in a £0 invoice or would they have to do something internally to account for this "purchase"?
If this is (in principle) possible to do, then I can of course have my lawyers review the wording I use to express it - at this point I really just want to know if it's possible in law to do something like this. Any help much appreciated.
Just to be clear (in response to comments): I'm asking about a legal principle/construct - to see if an idea is worth pursuing. I'm not asking for anyone to word a contract or agreement.
Also in response to comments and answers: A license is probably a better expression than a transfer for what I'm looking to achieve here.