PureOS is based on Debian, so you can follow the instructions on this page (follow the Ubuntu and Mint path):
https://github.com/monero-project/monero-gui
- Install Monero dependencies For Ubuntu and Mint
sudo apt install build-essential cmake libboost-all-dev miniupnpc libunbound-dev graphviz doxygen libunwind8-dev pkg-config libssl-dev libzmq3-dev
- Grab an up-to-date copy of the monero-gui repository
git clone https://github.com/monero-project/monero-gui.git
- Go into the repository
cd monero-gui
- Install the GUI Dependencies
For Ubuntu 16.04+ x64
sudo apt install qtbase5-dev qt5-default qtdeclarative5-dev qml-module-qtquick-controls qml-module-qtquick-xmllistmodel qttools5-dev-tools qml-module-qtquick-dialogs qml-module-qt-labs-settings libqt5qml-graphicaleffects
Optional : To build the flag WITH_SCANNER
For Ubuntu and Mint
sudo apt install qtmultimedia5-dev qml-module-qtmultimedia libzbar-dev
- Build the GUI
For Ubuntu and Mint
./build.sh
The executable can be found in the build/release/bin folder.
Hope it helps!