Have a look at this Webpage - I beleive it does exactly what you want.
Text content added below for completeness.
One thing I don’t like about Kaspersky product is after installing, it takes a very long time to fully update the program modules and bases files. Currently if you do a fresh installation of the latest version of Kaspersky 220.127.116.116, you’ll still need to download around 18MB. It’s not big but the problem is Kaspersky update servers are painfully slow… Combined with my customer’s place where the internet speed is crawling like a snail, I can never get to update Kaspersky to use the latest program modules and bases. It’s pointless having one of the best antivirus installed on the computer but without updating it.
Fortunately Kaspersky has came up with a very useful official tool that is able to create a “mirror” of the Kaspersky Lab’s update servers. This is very useful when you are like me who runs around installing Kaspersky products on other people’s computer. You can also use this if you have a few Kaspersky product installed in your network and you want all of the computers to update locally instead of individually downloading from Kaspersky and wasting your bandwidth. Most of the time this can only be done on “enterprise/corporate” version of the software but now you can also do it on desktop version.
Basically this tool is called Kaspersky Updater and is able to automatically download latest anti-virus bases and application program modules for all Kaspersky applications. For my case, I save the downloaded files in my USB flash drive, install Kaspersky software, and configure it to grab the updates from my USB flash drive.
If you want your computers in your network to grab the latest definition from a local server, then all you need to do is to share the “Updates” folder and configure Kaspersky to get it from the folder that you just shared. Best part is Kaspersky Updater supports scheduled updates so it can run automatically without you checking on it all the time.
There are 2 parts that in the whole process that is to run Kaspersky Updater to download latest bases and modules and finally configure the computer to grab the updates locally. Here are the steps on how to use Kaspersky Updater.
Download the latest version of Kaspersky Updater GUI from official Kaspersky forum. You will need to sign up in order to download. The official stable version of GUI is v18.104.22.168 but I prefer to use v22.214.171.124 Beta because it has Schedule feature.
Download the latest version of Update Utility. Extract both GUI and Updater and make sure they are in the same directory.
Select “Download databases for the selected products” and check the boxes according to which version of base that you want to download. Click Apply then Start and it will start to download. First time will take quite a while to complete downloading but after that it should only a few seconds because it supports incremental updates.
Optional: If you want to schedule Kaspersky Updater to automatically download the latest bases, then click the Schedule button, and choose whether to you want it to run automatically every few hours, days or weeks. Click Apply. For some weird reasons I am getting an error “not a valid date and time”. Well it’s still in beta and hopefully they’ll fix this bug.
Now you’ll have to configure Kaspersky software to grab the updates from your USB flash drive or from the shared folder. Click Settings > click Update on the left pane > Click the Settings button > click Add, browse the location of the Updates folder and click OK > Uncheck Kaspersky Lab’s update servers > and click OK to close the update settings window. You can refer to the animation below on how to do that.
First time updating directly from Kaspersky Lab’s online update server takes about more than an hour but when done locally, it takes less than a minute to download 18MB of updates