Can my xubuntu installation be converted to standard Ubuntu?

You'll simply need to install the ubuntu-desktop meta-package. This installs all the nessisary packages for a "Vanilla" Ubuntu Desktop. sudo apt-get install ubuntu-desktop Once this has been completed you can restart your computer. At the login screen you can switch from XFCE to Ubuntu Desktop under the Session dropdown. Doing so will load the Gnome desktop.

If you're satisfied with Ubuntu Desktop and wish to remove xubuntu you can always remove the meta package xubuntu-desktop which will remove the meta-package. If you wish to remove all the packages from the xubuntu-desktop meta package you'll have to remove those by hand. An updated list of all the packages by distrobution is available simply copy the line for your version of Ubuntu

Install ubuntu-desktop. To uninstall xubuntu, follow these guidelines: (select the right ubuntu version first) http://www.psychocats.net/ubuntu/puregnome

Since xubuntu-destkop is a metapackage removing it will not remove the other underlying packages. The link above tells you which ones you need

You can simply install all standart ubuntu package with apt

sudo apt install ubuntu-desktop

Then when you feel good with your new environement

sudo apt purge xubuntu-desktop
sudo apt autoremove

And don't forget to reconfigure GDM3 login

sudo dpkg-reconfigure gdm3

Also you may want to change Ubuntu loading screen. It is realy easy, check this answer.

Finally reboot

sudo reboot