are the specs of this computer sufficient to run office 365 and open pdf files on the internet?

Keeping seeveral open Excel sheets and also several PDFs open at once will eat up resources like crazy,
What problems is the user reporting? pdf reader crashes? PC freezes? , the problems can be many and maybe you dont need new equipment, but try to keep the files opened at same time to a minimum, specially if you are using a browser to view them instead of a reader like acrobat or foxit (I prefer foxit myself, has proven to crash less than adobes own reader), as for the specs of the equipment those should suffice for regular use, but heavy duty use is what you are talking about, and in that case I believe that you need to change the way to do things instead of the equipment.

I feel the same way but when your dealing with a complainer, sometimes they are never satisfied.  I just wanted an expert comment to have in my back pocket if they guy says that this computer I am going to buy still is not good enough.

The computer you describe is plenty powerful enough for the type of work described.

I am a long-time Excel power user, and am currently running Windows Excel 2016/Office 365 on a virtual machine on my MacBook Pro. The virtual machine is provisioned with 8 GB of RAM (though I wish it had 16 GB), and runs perhaps at 75% of the speed of Excel on a similar spec'd computer without a virtual machine. I write VBA code, and know that if I am happy with the speed it runs, my client will be delighted.

I have been using virtual machines to run Windows Excel since 2001, and performance became acceptably fast by 2003. As a mechanical engineer, I do a fair bit of VBA coding in my day job, and have answered over 10,000 Excel questions here on Experts-Exchange since 2003. None of my computers over the past two decades are as powerful as the one described in the question.

When you install Office 365 for the employee, you get a choice of using either 32-bit or 64-bit. Both versions are available on the install media/download--but 32-bit is usually the default. Please consider choosing 64-bit Office, which lets Excel use all the RAM on the computer (limit is thousands of GB). The 32-bit install limits Excel to 4 GB of memory, no matter how much you have installed on the computer. That memory must be shared by the Excel application, all the add-ins, and all the workbooks. When you get a message about this computer does not have enough resources to undo an operation, that's a hint that you are running into the 4 GB limit. With 64-bit Excel on my virtual machine, I never get a "this operation cannot be completed" message when working with huge workbooks; I used to see them from time to time when I was running 32-bit Excel.

Ask if your employee uses third-party Excel add-ins. If so, he may run into conflicts if they haven't been updated to run on 64-bit Excel. Developers of all the most popular add-ins have updated their products, but developers of less popular ones may not have felt enough market pressure to do so.

Unless it has changed, the trackpad on HP laptops is not very good. It picks up the heel of your hand and moves the cursor unexpectedly while you are typing. I used HP laptops from 2003 to 2009, and turned their trackpad off (a setting that HP gives you) and used an external mouse instead.

If your employee is viewing large CAD drawings, I advise asking a separate question about whether the computer is powerful enough. It may be that using a different viewer or CAD package would help.

Better to understand exactly what is the problem. Any i7 system should be enough... and 16GB is more than enough for most cases.
Also keep in mind that if they are using this machine to RUN remote desktop and the compute is being done on the host and there are still problems, then it could be another problem.

If he's trying to open and edit large Excel files over the connection rather than using OneDrive to sync them locally, update and then sync back, that may explain why they are unhappy?