My colleagure suggests that linearity of a HPLC UV method should be confirmed with an UV photometer. That is,to use the same set of standard solutions measure the learity on both HPLC UV and UV photometer.
If results from the UV photometer indicates that the higher concentration of the standard solutions is saturated, then the HPLC UV detector is saturated even the HPLC shown linea regression R2>0.9999,the peak intensity is less than 0.3 V (instrument up limit 2.0V) or the peak shape is sharp.
I belive that HPLC UV cell is diffrent from UV photometer in terms of size, flow vs static, sensitivity, etc. They can not be used for comparing for the purpose of determine if a solution is saturated on HPLC detector. My colleague strongly belive that the enrgy from both cell should be same regardless the size difference because e=hv and thus, results from both should be same.
Is it a common practice to confirm linearity of HPLC UV method with a UV photometer? Is it proper to determine if the HPLC UV is saturated by a UV Photometer?

You are correct and your coworker is a little misguided. See the earlier discussion titled 'Detector saturation' for more info.

In addition to earlier discussed "detector saturation" you pointed very interesting problem of "flow vs. static." How it is important, you can test on your HPLC detector. If I decrease flow, I obtain higher signal (both by UV and RI detectors)!

If you are getting a higher signal (more absorbance, taller peaks) with a lower flow, then column resolution is higher at that flow, or the detector response time was too slow for the faster flow rate, and the detector was simply missing the top of the peak. Some detectors can be set to very long response times. Since you observe the same thing from both detectors, it is probably column resolution improvement. I would guess that peak areas are similar for both flow rates.

Just make sure that the area (or height)/response curves are linear over the concentration range you plan to use, and your data will be ok. At the low absorbance level indicated in the original post, 0.3 AU, the system is a VERY long way from being saturated.

To answer the original post directly, it is not reasonable to expect a UV spectrophotometer to give the same response as a UV HPLC detector, because of band spreading from the flow and column, dilution as a result of injection, etc.

If, however, a chemist simply pumped the same standard solution through the LC detector (no column, no mobile phase, no injection) that was presented to the UV spectometer, with equal cell path lengths the results would, indeed, be the 'same'. But if this were the case, the LC would not be needed in the first place.

One of the great advantages of HPLC vs. GC is the long linear range of most LC detectors, and is one of the reasons we are converting GC analyses to HPLC as fast as we can.

if one is quantifying using HPLC method, must the concntrations of the analyte lie in linearity range?

In practice, yes.

In principle, if you have an accurate fitting function for the non-linear response, you could use that. The difficulties involved are such that it is almost never used for UV. For other detector types which have inherently narrow linear ranges, it is not uncommon.

is "high presssure liquid chromatography" the same as liquid chromatography?

it's a subset (i.e., all high pressure liquid chromatography is liquid chromatography, but not all liquid chromatography is high pressure liquid chromatography).