You can try creating a dictionary from columns ['CheckStringHere','AssociatedValue1']
and replace values from StringToCheck
column:
d = dict(df[['CheckStringHere','AssociatedValue1']].to_numpy())
df['FromNumber'] = df['StringToCheck'].replace(d)
#or df['FromNumber'] = df['StringToCheck'].map(d).fillna(df['FromNumber'])
print(df)
StringToCheck FromNumber ToNumber CheckStringHere AssociatedValue1 \
0 10T 56 AAA_ER
1 125T 16 FGGR_DBC
2 10T 56
3 125T 16
AssociatedValue2
0
1
2 58
3 24
2
solved Search for column values in another column and assign a value from the next column from the row found to another column