Adds a GMP to the 5'-end of tRNA(His) after transcription and RNase P cleavage. This step is essential for proper recognition of the tRNA and for the fidelity of protein synthesis (Probable). Also functions as a guanyl-nucleotide exchange factor/GEF for the MFN1 and MFN2 mitofusins thereby regulating mitochondrial fusion (PubMed:25008184, PubMed:27307223). By regulating both mitochondrial dynamics and bioenergetic function, it contributes to cell survival following oxidative stress (PubMed:25008184, PubMed:27307223). {ECO:0000269|PubMed:25008184, ECO:0000269|PubMed:27307223, ECO:0000305|PubMed:21059936}. This is the function of THG1L (tRNA-histidine guanylyltransferase 1 like, Ensembl gene identifier ENSG00000113272).