The printer can only print blues that are in gamut. If they are a good printer, they have a good Colour Management workflow in place and should be able to get as close as they can get, but as Scotty would say, you can't change the laws of physics! Your client will have to accept that they can't get what they want. Their best bet is to have the blue printed as a spot Pantone colour which may get you closer to what they desire, but that means you are paying for a 5-colour printing job. As far as getting brighter blues in CMYK, well, you can't. I suggest you invest in a Pantone swatch book that shows CMYK matches so your client can see what is and what is not possible. Here's the deal. The conversion fron LAB to CMYK can be wildly different in practically every scenario, depending on the Color Management settings used along the way, as well as the actual printing process used by your printer, etc. If it this was printed before from the same file, the CMYK mix that was previously printed WILL be different today if the profiles assigned to them then were different. It will be impossible to give your printer a new CMYK file with values that create that previous blue if you don't know what the values ended up being! It also depends on where the conversion happens. If you created a PDF that converts the colours at your end, then you've already baked in a CMYK mix for that blue based on the colour profiles you have in your OWN workflow. If the PDF was created where the colours are left as is, then the CMYK conversion will happen in your printer's workflow. Going forward, you should always select colours that are in gamut of your intended printing process, or accept the fact that there will be differences. e.g. If you are working with Pantone colours (e.g. Spot Coated swatches, which are LAB), many of these are also out of gamut as they were always intended to be an actual ink used in printing (mixed using several base inks other than CMYK (there's about 15 of them) that create a wide vibrant set of colours). Pantone has attempted many solutions over the years to help out the current digital workflows and the latest is a set of ink swatches called Color Bridge that are based in CMYK, so if you use those, you should be able to see and keep a consistent colour match.
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