I agree; You can speculate that the father named on the 1912 Birth Cert is a "phantom" to cover up a "mistake" , but when she comes to marry in 1915 how does she undo the "cover up" ? - by claiming to be widowed. By then its war time , so perhaps the vicar performing the marriage "took her word".

Did she know this DAWSON and simply take his "name" as a husband knowing he was already dead ?

Name: Charles Henry Dawson
Estimated birth year: abt 1885
Year of Registration: 1906
Quarter of Registration: Apr-May-Jun
Age at Death: 21
District: Henley
County: Buckinghamshire, Berkshire, Oxfordshire
Volume: 3a
Page: 481

The "first" marriage if it exists should be in the BMD registers (ancestry allows us to see England and Wales) - could the marriage have been in Scotland or Ireland ? or elsewhere.

Where is the "dead" Henry Charles DAWSON ?

Name: Henry C Dawson
Estimated birth year: abt 1885
Year of Registration: 1912
Quarter of Registration: Jan-Feb-Mar
Age at Death: 27
District: Middlesbrough (1875-1968)
County: Yorkshire - North Riding
Volume: 9d
Page: 836