You need the following tools: Sysinternal suite.

First, run a elevated command prompt by right clicking on cmd.exe -> Run as Administrator…

The have a root cmd.exe by typing:

psexec -s -i cmd.exe

You can now mount and save the credential of your share:

net use Z: \\yourshare\folder /savecred /persistent:yes

You will be prompted for you password. You can verify that the password have been saved with the command:

cmdkey /list

Last step is to create a task that run at startup with the SYSTEM user and the following content:

net use Z: \\yourshare\folder