Some people memorise a formula but I would suggest you learn the fundamentals if you are new to this.
Let’s say your molecular weight is 100. It follows that 100g/L gives a 1M solution. If mol weight is 200, then 200g/L would be 1M. From this position you can easily extrapolate to mg or ug, and other volumes.
In the case of your assay, I would say it is quite unusual to measure ug released, though it is perfectly valid and your standard curve x axis can use ug, pmol, nmol, mM, or whatever you prefer.
It is sometimes easier to set up the curve using the unit you are most interested in, but you can always interconvert if you know that 1L of a 1M solution contains ‘x’ g of substance, where x = mol weight.
If the activity measures the liberation of tyrosine then you have to use tyrosine MW to convert units. Tyr MW is 181.19 Da ( 1 Da corresponds to g/mol and µg/µmol). So divide you result expressed in µg/mL by 181.19 and you'll get µmol/mL.