After a reboot of the server we noticed that the SQL service is only using half of the memory.
SQL server will use memory as an when needed. Once you reboot your instance, it will take sql server some time to ramp up (bringing pages in the buffer pool), since a reboot will trash all the query plans and reset DMV data.
Min server memory controls the minimum amount of Physical memory that sql server will try to keep committed. When the SQL Server service starts, it does not acquire all the memory configured in Min Server Memory but instead starts with only the minimum required, growing as necessary. Once memory usage has increased beyond the Min Server Memory setting, SQL Server won’t release any memory below that amount.
Let your workload run and sql server will eventually reach your MAX MEMORY setting.
Check : How to determine ideal memory for instance?
On the instance in Properties > General > Memory it shows 131072 MB
This is the total memory available to the instance i.e. It lists the amount of RAM installed on the server.
On the instance in Properties > Memory > Max Server Memory it shows 2147483647 MB
The is the MAX memory and you should change it away from the default (use up all memory)
Also, from sql server 2012, Memory management has gone some major changes.
Setting max server memory becomes more straightforward with SQL Server 2012. The redesigned Memory Manager takes a central role in providing page allocations for the other components, and the max server memory setting governs all memory manager allocations.